diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 155ef316..eef12a15 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -24,6 +24,7 @@ jobs:
         run: |
           git clone --depth 1 https://github.com/docker-library/bashbrew.git -b master ~/bashbrew
           strategy="$(~/bashbrew/scripts/github-actions/generate.sh)"
+          strategy="$(~/bashbrew/scripts/github-actions/munge-i386.sh -c <<<"$strategy")"
           jq . <<<"$strategy" # sanity check / debugging aid
           echo "::set-output name=strategy::$strategy"
 
diff --git a/1.15/alpine3.12/Dockerfile b/1.15/alpine3.12/Dockerfile
index c85b4e70..3c739da2 100644
--- a/1.15/alpine3.12/Dockerfile
+++ b/1.15/alpine3.12/Dockerfile
@@ -27,23 +27,30 @@ RUN set -eux; \
 		musl-dev \
 		openssl \
 	; \
-	export \
-# set GOROOT_BOOTSTRAP such that we can actually build Go
-		GOROOT_BOOTSTRAP="$(go env GOROOT)" \
-# ... and set "cross-building" related vars to the installed system's values so that we create a build targeting the proper arch
-# (for example, if our build host is GOARCH=amd64, but our build env/image is GOARCH=386, our build needs GOARCH=386)
-		GOOS="$(go env GOOS)" \
-		GOARCH="$(go env GOARCH)" \
-		GOHOSTOS="$(go env GOHOSTOS)" \
-		GOHOSTARCH="$(go env GOHOSTARCH)" \
-	; \
-# also explicitly set GO386 and GOARM if appropriate
-# https://github.com/docker-library/golang/issues/184
 	apkArch="$(apk --print-arch)"; \
 	case "$apkArch" in \
-		armhf) export GOARM='6' ;; \
-		armv7) export GOARM='7' ;; \
-		x86) export GO386='387' ;; \
+		'x86_64') \
+			export GOARCH='amd64' GOOS='linux'; \
+			;; \
+		'armhf') \
+			export GOARCH='arm' GOARM='6' GOOS='linux'; \
+			;; \
+		'armv7') \
+			export GOARCH='arm' GOARM='7' GOOS='linux'; \
+			;; \
+		'aarch64') \
+			export GOARCH='arm64' GOOS='linux'; \
+			;; \
+		'x86') \
+			export GO386='387' GOARCH='386' GOOS='linux'; \
+			;; \
+		'ppc64le') \
+			export GOARCH='ppc64le' GOOS='linux'; \
+			;; \
+		's390x') \
+			export GOARCH='s390x' GOOS='linux'; \
+			;; \
+		*) echo >&2 "error: unsupported architecture '$apkArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
 	\
 # https://github.com/golang/go/issues/38536#issuecomment-616897960
@@ -65,13 +72,21 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-	eval "$goEnv"; \
-	[ -n "$GOOS" ]; \
-	[ -n "$GOARCH" ]; \
 	( \
 		cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+		export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+# https://github.com/docker-library/golang/issues/359 -> https://github.com/golang/go/issues/44500
+# (once our Alpine base has Go 1.16, we can remove this hack)
+			GO386= ./bootstrap.bash; \
+			export GOROOT_BOOTSTRAP="/usr/local/go-$GOOS-$GOARCH-bootstrap"; \
+			"$GOROOT_BOOTSTRAP/bin/go" version; \
+		fi; \
 		./make.bash; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+			rm -rf "$GOROOT_BOOTSTRAP"; \
+		fi; \
 	); \
 	\
 	apk del --no-network .build-deps; \
diff --git a/1.15/alpine3.13/Dockerfile b/1.15/alpine3.13/Dockerfile
index 82445cf3..9836c04f 100644
--- a/1.15/alpine3.13/Dockerfile
+++ b/1.15/alpine3.13/Dockerfile
@@ -27,23 +27,30 @@ RUN set -eux; \
 		musl-dev \
 		openssl \
 	; \
-	export \
-# set GOROOT_BOOTSTRAP such that we can actually build Go
-		GOROOT_BOOTSTRAP="$(go env GOROOT)" \
-# ... and set "cross-building" related vars to the installed system's values so that we create a build targeting the proper arch
-# (for example, if our build host is GOARCH=amd64, but our build env/image is GOARCH=386, our build needs GOARCH=386)
-		GOOS="$(go env GOOS)" \
-		GOARCH="$(go env GOARCH)" \
-		GOHOSTOS="$(go env GOHOSTOS)" \
-		GOHOSTARCH="$(go env GOHOSTARCH)" \
-	; \
-# also explicitly set GO386 and GOARM if appropriate
-# https://github.com/docker-library/golang/issues/184
 	apkArch="$(apk --print-arch)"; \
 	case "$apkArch" in \
-		armhf) export GOARM='6' ;; \
-		armv7) export GOARM='7' ;; \
-		x86) export GO386='387' ;; \
+		'x86_64') \
+			export GOARCH='amd64' GOOS='linux'; \
+			;; \
+		'armhf') \
+			export GOARCH='arm' GOARM='6' GOOS='linux'; \
+			;; \
+		'armv7') \
+			export GOARCH='arm' GOARM='7' GOOS='linux'; \
+			;; \
+		'aarch64') \
+			export GOARCH='arm64' GOOS='linux'; \
+			;; \
+		'x86') \
+			export GO386='387' GOARCH='386' GOOS='linux'; \
+			;; \
+		'ppc64le') \
+			export GOARCH='ppc64le' GOOS='linux'; \
+			;; \
+		's390x') \
+			export GOARCH='s390x' GOOS='linux'; \
+			;; \
+		*) echo >&2 "error: unsupported architecture '$apkArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
 	\
 # https://github.com/golang/go/issues/38536#issuecomment-616897960
@@ -65,13 +72,21 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-	eval "$goEnv"; \
-	[ -n "$GOOS" ]; \
-	[ -n "$GOARCH" ]; \
 	( \
 		cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+		export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+# https://github.com/docker-library/golang/issues/359 -> https://github.com/golang/go/issues/44500
+# (once our Alpine base has Go 1.16, we can remove this hack)
+			GO386= ./bootstrap.bash; \
+			export GOROOT_BOOTSTRAP="/usr/local/go-$GOOS-$GOARCH-bootstrap"; \
+			"$GOROOT_BOOTSTRAP/bin/go" version; \
+		fi; \
 		./make.bash; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+			rm -rf "$GOROOT_BOOTSTRAP"; \
+		fi; \
 	); \
 	\
 	apk del --no-network .build-deps; \
diff --git a/1.15/buster/Dockerfile b/1.15/buster/Dockerfile
index e254a692..e53f88db 100644
--- a/1.15/buster/Dockerfile
+++ b/1.15/buster/Dockerfile
@@ -22,47 +22,50 @@ ENV GOLANG_VERSION 1.15.8
 RUN set -eux; \
 	\
 	dpkgArch="$(dpkg --print-architecture)"; \
+	url=; \
 	case "${dpkgArch##*-}" in \
 		'amd64') \
-			arch='linux-amd64'; \
 			url='https://storage.googleapis.com/golang/go1.15.8.linux-amd64.tar.gz'; \
 			sha256='d3379c32a90fdf9382166f8f48034c459a8cc433730bc9476d39d9082c94583b'; \
 			;; \
+		'armel') \
+			export GOARCH='arm' GOARM='5' GOOS='linux'; \
+			;; \
 		'armhf') \
-			arch='linux-armv6l'; \
 			url='https://storage.googleapis.com/golang/go1.15.8.linux-armv6l.tar.gz'; \
 			sha256='708c398cb9e5029cfd5b654370978bf0e797d4d4a71153c06c7378db7e249a53'; \
 			;; \
 		'arm64') \
-			arch='linux-arm64'; \
 			url='https://storage.googleapis.com/golang/go1.15.8.linux-arm64.tar.gz'; \
 			sha256='0e31ea4bf53496b0f0809730520dee98c0ae5c530f3701a19df0ba0a327bf3d2'; \
 			;; \
 		'i386') \
-			arch='linux-386'; \
 			url='https://storage.googleapis.com/golang/go1.15.8.linux-386.tar.gz'; \
 			sha256='a0cc9df6d04f89af8396278d171087894a453a03a950b0f60a4ac18b480f758f'; \
 			;; \
+		'mips64el') \
+			export GOARCH='mips64le' GOOS='linux'; \
+			;; \
 		'ppc64el') \
-			arch='linux-ppc64le'; \
 			url='https://storage.googleapis.com/golang/go1.15.8.linux-ppc64le.tar.gz'; \
 			sha256='c6ddeab22b23ee33f5e8f06f9667e2092f48dbc6d5db553a66f7fe21da73fbfa'; \
 			;; \
 		's390x') \
-			arch='linux-s390x'; \
 			url='https://storage.googleapis.com/golang/go1.15.8.linux-s390x.tar.gz'; \
 			sha256='ba922f54fe99dee3246705bacbfac27fa88375439025429297aa1e9caf3f2297'; \
 			;; \
-		*) \
-# https://github.com/golang/go/issues/38536#issuecomment-616897960
-			arch='src'; \
-			url='https://storage.googleapis.com/golang/go1.15.8.src.tar.gz'; \
-			sha256='540c0ab7781084d124991321ed1458e479982de94454a98afab6acadf38497c2'; \
-			echo >&2; \
-			echo >&2 "warning: current architecture ($dpkgArch) does not have a corresponding Go binary release; will be building from source"; \
-			echo >&2; \
-			;; \
+		*) echo >&2 "error: unsupported architecture '$dpkgArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
+	build=; \
+	if [ -z "$url" ]; then \
+# https://github.com/golang/go/issues/38536#issuecomment-616897960
+		build=1; \
+		url='https://storage.googleapis.com/golang/go1.15.8.src.tar.gz'; \
+		sha256='540c0ab7781084d124991321ed1458e479982de94454a98afab6acadf38497c2'; \
+		echo >&2; \
+		echo >&2 "warning: current architecture ($dpkgArch) does not have a corresponding Go binary release; will be building from source"; \
+		echo >&2; \
+	fi; \
 	\
 	wget -O go.tgz.asc "$url.asc" --progress=dot:giga; \
 	wget -O go.tgz "$url" --progress=dot:giga; \
@@ -79,17 +82,15 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	if [ "$arch" = 'src' ]; then \
+	if [ -n "$build" ]; then \
 		savedAptMark="$(apt-mark showmanual)"; \
 		apt-get update; \
 		apt-get install -y --no-install-recommends golang-go; \
 		\
-		goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-		eval "$goEnv"; \
-		[ -n "$GOOS" ]; \
-		[ -n "$GOARCH" ]; \
 		( \
 			cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+			export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
 			./make.bash; \
 		); \
 		\
diff --git a/1.16/alpine3.12/Dockerfile b/1.16/alpine3.12/Dockerfile
index c980dcf9..2620c2cb 100644
--- a/1.16/alpine3.12/Dockerfile
+++ b/1.16/alpine3.12/Dockerfile
@@ -27,23 +27,30 @@ RUN set -eux; \
 		musl-dev \
 		openssl \
 	; \
-	export \
-# set GOROOT_BOOTSTRAP such that we can actually build Go
-		GOROOT_BOOTSTRAP="$(go env GOROOT)" \
-# ... and set "cross-building" related vars to the installed system's values so that we create a build targeting the proper arch
-# (for example, if our build host is GOARCH=amd64, but our build env/image is GOARCH=386, our build needs GOARCH=386)
-		GOOS="$(go env GOOS)" \
-		GOARCH="$(go env GOARCH)" \
-		GOHOSTOS="$(go env GOHOSTOS)" \
-		GOHOSTARCH="$(go env GOHOSTARCH)" \
-	; \
-# also explicitly set GO386 and GOARM if appropriate
-# https://github.com/docker-library/golang/issues/184
 	apkArch="$(apk --print-arch)"; \
 	case "$apkArch" in \
-		armhf) export GOARM='6' ;; \
-		armv7) export GOARM='7' ;; \
-		x86) export GO386='softfloat' ;; \
+		'x86_64') \
+			export GOARCH='amd64' GOOS='linux'; \
+			;; \
+		'armhf') \
+			export GOARCH='arm' GOARM='6' GOOS='linux'; \
+			;; \
+		'armv7') \
+			export GOARCH='arm' GOARM='7' GOOS='linux'; \
+			;; \
+		'aarch64') \
+			export GOARCH='arm64' GOOS='linux'; \
+			;; \
+		'x86') \
+			export GO386='softfloat' GOARCH='386' GOOS='linux'; \
+			;; \
+		'ppc64le') \
+			export GOARCH='ppc64le' GOOS='linux'; \
+			;; \
+		's390x') \
+			export GOARCH='s390x' GOOS='linux'; \
+			;; \
+		*) echo >&2 "error: unsupported architecture '$apkArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
 	\
 # https://github.com/golang/go/issues/38536#issuecomment-616897960
@@ -65,13 +72,21 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-	eval "$goEnv"; \
-	[ -n "$GOOS" ]; \
-	[ -n "$GOARCH" ]; \
 	( \
 		cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+		export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+# https://github.com/docker-library/golang/issues/359 -> https://github.com/golang/go/issues/44500
+# (once our Alpine base has Go 1.16, we can remove this hack)
+			GO386= ./bootstrap.bash; \
+			export GOROOT_BOOTSTRAP="/usr/local/go-$GOOS-$GOARCH-bootstrap"; \
+			"$GOROOT_BOOTSTRAP/bin/go" version; \
+		fi; \
 		./make.bash; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+			rm -rf "$GOROOT_BOOTSTRAP"; \
+		fi; \
 	); \
 	\
 	apk del --no-network .build-deps; \
diff --git a/1.16/alpine3.13/Dockerfile b/1.16/alpine3.13/Dockerfile
index 8dd40ef8..fda850a7 100644
--- a/1.16/alpine3.13/Dockerfile
+++ b/1.16/alpine3.13/Dockerfile
@@ -27,23 +27,30 @@ RUN set -eux; \
 		musl-dev \
 		openssl \
 	; \
-	export \
-# set GOROOT_BOOTSTRAP such that we can actually build Go
-		GOROOT_BOOTSTRAP="$(go env GOROOT)" \
-# ... and set "cross-building" related vars to the installed system's values so that we create a build targeting the proper arch
-# (for example, if our build host is GOARCH=amd64, but our build env/image is GOARCH=386, our build needs GOARCH=386)
-		GOOS="$(go env GOOS)" \
-		GOARCH="$(go env GOARCH)" \
-		GOHOSTOS="$(go env GOHOSTOS)" \
-		GOHOSTARCH="$(go env GOHOSTARCH)" \
-	; \
-# also explicitly set GO386 and GOARM if appropriate
-# https://github.com/docker-library/golang/issues/184
 	apkArch="$(apk --print-arch)"; \
 	case "$apkArch" in \
-		armhf) export GOARM='6' ;; \
-		armv7) export GOARM='7' ;; \
-		x86) export GO386='softfloat' ;; \
+		'x86_64') \
+			export GOARCH='amd64' GOOS='linux'; \
+			;; \
+		'armhf') \
+			export GOARCH='arm' GOARM='6' GOOS='linux'; \
+			;; \
+		'armv7') \
+			export GOARCH='arm' GOARM='7' GOOS='linux'; \
+			;; \
+		'aarch64') \
+			export GOARCH='arm64' GOOS='linux'; \
+			;; \
+		'x86') \
+			export GO386='softfloat' GOARCH='386' GOOS='linux'; \
+			;; \
+		'ppc64le') \
+			export GOARCH='ppc64le' GOOS='linux'; \
+			;; \
+		's390x') \
+			export GOARCH='s390x' GOOS='linux'; \
+			;; \
+		*) echo >&2 "error: unsupported architecture '$apkArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
 	\
 # https://github.com/golang/go/issues/38536#issuecomment-616897960
@@ -65,13 +72,21 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-	eval "$goEnv"; \
-	[ -n "$GOOS" ]; \
-	[ -n "$GOARCH" ]; \
 	( \
 		cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+		export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+# https://github.com/docker-library/golang/issues/359 -> https://github.com/golang/go/issues/44500
+# (once our Alpine base has Go 1.16, we can remove this hack)
+			GO386= ./bootstrap.bash; \
+			export GOROOT_BOOTSTRAP="/usr/local/go-$GOOS-$GOARCH-bootstrap"; \
+			"$GOROOT_BOOTSTRAP/bin/go" version; \
+		fi; \
 		./make.bash; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+			rm -rf "$GOROOT_BOOTSTRAP"; \
+		fi; \
 	); \
 	\
 	apk del --no-network .build-deps; \
diff --git a/1.16/buster/Dockerfile b/1.16/buster/Dockerfile
index 59049394..baa3b134 100644
--- a/1.16/buster/Dockerfile
+++ b/1.16/buster/Dockerfile
@@ -22,47 +22,50 @@ ENV GOLANG_VERSION 1.16
 RUN set -eux; \
 	\
 	dpkgArch="$(dpkg --print-architecture)"; \
+	url=; \
 	case "${dpkgArch##*-}" in \
 		'amd64') \
-			arch='linux-amd64'; \
 			url='https://storage.googleapis.com/golang/go1.16.linux-amd64.tar.gz'; \
 			sha256='013a489ebb3e24ef3d915abe5b94c3286c070dfe0818d5bca8108f1d6e8440d2'; \
 			;; \
+		'armel') \
+			export GOARCH='arm' GOARM='5' GOOS='linux'; \
+			;; \
 		'armhf') \
-			arch='linux-armv6l'; \
 			url='https://storage.googleapis.com/golang/go1.16.linux-armv6l.tar.gz'; \
 			sha256='d1d9404b1dbd77afa2bdc70934e10fbfcf7d785c372efc29462bb7d83d0a32fd'; \
 			;; \
 		'arm64') \
-			arch='linux-arm64'; \
 			url='https://storage.googleapis.com/golang/go1.16.linux-arm64.tar.gz'; \
 			sha256='3770f7eb22d05e25fbee8fb53c2a4e897da043eb83c69b9a14f8d98562cd8098'; \
 			;; \
 		'i386') \
-			arch='linux-386'; \
 			url='https://storage.googleapis.com/golang/go1.16.linux-386.tar.gz'; \
 			sha256='ea435a1ac6d497b03e367fdfb74b33e961d813883468080f6e239b3b03bea6aa'; \
 			;; \
+		'mips64el') \
+			export GOARCH='mips64le' GOOS='linux'; \
+			;; \
 		'ppc64el') \
-			arch='linux-ppc64le'; \
 			url='https://storage.googleapis.com/golang/go1.16.linux-ppc64le.tar.gz'; \
 			sha256='27a1aaa988e930b7932ce459c8a63ad5b3333b3a06b016d87ff289f2a11aacd6'; \
 			;; \
 		's390x') \
-			arch='linux-s390x'; \
 			url='https://storage.googleapis.com/golang/go1.16.linux-s390x.tar.gz'; \
 			sha256='be4c9e4e2cf058efc4e3eb013a760cb989ddc4362f111950c990d1c63b27ccbe'; \
 			;; \
-		*) \
-# https://github.com/golang/go/issues/38536#issuecomment-616897960
-			arch='src'; \
-			url='https://storage.googleapis.com/golang/go1.16.src.tar.gz'; \
-			sha256='7688063d55656105898f323d90a79a39c378d86fe89ae192eb3b7fc46347c95a'; \
-			echo >&2; \
-			echo >&2 "warning: current architecture ($dpkgArch) does not have a corresponding Go binary release; will be building from source"; \
-			echo >&2; \
-			;; \
+		*) echo >&2 "error: unsupported architecture '$dpkgArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
+	build=; \
+	if [ -z "$url" ]; then \
+# https://github.com/golang/go/issues/38536#issuecomment-616897960
+		build=1; \
+		url='https://storage.googleapis.com/golang/go1.16.src.tar.gz'; \
+		sha256='7688063d55656105898f323d90a79a39c378d86fe89ae192eb3b7fc46347c95a'; \
+		echo >&2; \
+		echo >&2 "warning: current architecture ($dpkgArch) does not have a corresponding Go binary release; will be building from source"; \
+		echo >&2; \
+	fi; \
 	\
 	wget -O go.tgz.asc "$url.asc" --progress=dot:giga; \
 	wget -O go.tgz "$url" --progress=dot:giga; \
@@ -79,17 +82,15 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	if [ "$arch" = 'src' ]; then \
+	if [ -n "$build" ]; then \
 		savedAptMark="$(apt-mark showmanual)"; \
 		apt-get update; \
 		apt-get install -y --no-install-recommends golang-go; \
 		\
-		goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-		eval "$goEnv"; \
-		[ -n "$GOOS" ]; \
-		[ -n "$GOARCH" ]; \
 		( \
 			cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+			export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
 			./make.bash; \
 		); \
 		\
diff --git a/Dockerfile-alpine.template b/Dockerfile-alpine.template
index 55334f39..436bbded 100644
--- a/Dockerfile-alpine.template
+++ b/Dockerfile-alpine.template
@@ -21,23 +21,35 @@ RUN set -eux; \
 		musl-dev \
 		openssl \
 	; \
-	export \
-# set GOROOT_BOOTSTRAP such that we can actually build Go
-		GOROOT_BOOTSTRAP="$(go env GOROOT)" \
-# ... and set "cross-building" related vars to the installed system's values so that we create a build targeting the proper arch
-# (for example, if our build host is GOARCH=amd64, but our build env/image is GOARCH=386, our build needs GOARCH=386)
-		GOOS="$(go env GOOS)" \
-		GOARCH="$(go env GOARCH)" \
-		GOHOSTOS="$(go env GOHOSTOS)" \
-		GOHOSTARCH="$(go env GOHOSTARCH)" \
-	; \
-# also explicitly set GO386 and GOARM if appropriate
-# https://github.com/docker-library/golang/issues/184
 	apkArch="$(apk --print-arch)"; \
 	case "$apkArch" in \
-		armhf) export GOARM='6' ;; \
-		armv7) export GOARM='7' ;; \
-		x86) export GO386='{{ if env.version == "1.14" or env.version == "1.15" then "387" else "softfloat" end }}' ;; \
+{{
+	[
+		.arches | to_entries[]
+		| .key as $bashbrewArch
+		| (
+			{
+				amd64: "x86_64",
+				arm32v6: "armhf",
+				arm32v7: "armv7",
+				arm64v8: "aarch64",
+				i386: "x86",
+				ppc64le: "ppc64le",
+				s390x: "s390x",
+			} | .[$bashbrewArch] // ""
+		) as $apkArch
+		| select($apkArch != "")
+		| .value
+		| (
+-}}
+		{{ $apkArch | @sh }}) \
+			export {{ .env | to_entries | map(.key + "=" + (.value | @sh)) | join(" ") }}; \
+			;; \
+{{
+		)
+	] | add
+-}}
+		*) echo >&2 "error: unsupported architecture '$apkArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
 	\
 # https://github.com/golang/go/issues/38536#issuecomment-616897960
@@ -59,13 +71,21 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-	eval "$goEnv"; \
-	[ -n "$GOOS" ]; \
-	[ -n "$GOARCH" ]; \
 	( \
 		cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+		export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+# https://github.com/docker-library/golang/issues/359 -> https://github.com/golang/go/issues/44500
+# (once our Alpine base has Go 1.16, we can remove this hack)
+			GO386= ./bootstrap.bash; \
+			export GOROOT_BOOTSTRAP="/usr/local/go-$GOOS-$GOARCH-bootstrap"; \
+			"$GOROOT_BOOTSTRAP/bin/go" version; \
+		fi; \
 		./make.bash; \
+		if [ "${GO386:-}" = 'softfloat' ]; then \
+			rm -rf "$GOROOT_BOOTSTRAP"; \
+		fi; \
 	); \
 	\
 	apk del --no-network .build-deps; \
diff --git a/Dockerfile-debian.template b/Dockerfile-debian.template
index 7f98e20a..3b67dcdd 100644
--- a/Dockerfile-debian.template
+++ b/Dockerfile-debian.template
@@ -16,44 +16,52 @@ ENV GOLANG_VERSION {{ .version }}
 RUN set -eux; \
 	\
 	dpkgArch="$(dpkg --print-architecture)"; \
+	url=; \
 	case "${dpkgArch##*-}" in \
 {{
 	[
 		.arches | to_entries[]
-		| select(.value.arch | startswith("linux-"))
 		| .key as $bashbrewArch
 		| (
 			{
+				amd64: "amd64",
 				arm32v5: "armel",
 				arm32v7: "armhf",
 				arm64v8: "arm64",
+				i386: "i386",
 				mips64le: "mips64el",
 				ppc64le: "ppc64el",
-			}
-			| .[$bashbrewArch] // $bashbrewArch
+				s390x: "s390x",
+			} | .[$bashbrewArch] // ""
 		) as $dpkgArch
+		| select($dpkgArch != "")
 		| .value
 		| (
 -}}
 		{{ $dpkgArch | @sh }}) \
-			arch={{ .arch | @sh }}; \
+{{ if .url then ( -}}
 			url={{ .url | @sh }}; \
 			sha256={{ .sha256 | @sh }}; \
+{{ ) else ( -}}
+			export {{ .env | to_entries | map(.key + "=" + (.value | @sh)) | join(" ") }}; \
+{{ ) end -}}
 			;; \
 {{
 		)
 	] | add
 -}}
-		*) \
-# https://github.com/golang/go/issues/38536#issuecomment-616897960
-			arch='src'; \
-			url={{ .arches.src.url | @sh }}; \
-			sha256={{ .arches.src.sha256 | @sh }}; \
-			echo >&2; \
-			echo >&2 "warning: current architecture ($dpkgArch) does not have a corresponding Go binary release; will be building from source"; \
-			echo >&2; \
-			;; \
+		*) echo >&2 "error: unsupported architecture '$dpkgArch' (likely packaging update needed)"; exit 1 ;; \
 	esac; \
+	build=; \
+	if [ -z "$url" ]; then \
+# https://github.com/golang/go/issues/38536#issuecomment-616897960
+		build=1; \
+		url={{ .arches.src.url | @sh }}; \
+		sha256={{ .arches.src.sha256 | @sh }}; \
+		echo >&2; \
+		echo >&2 "warning: current architecture ($dpkgArch) does not have a corresponding Go binary release; will be building from source"; \
+		echo >&2; \
+	fi; \
 	\
 	wget -O go.tgz.asc "$url.asc" --progress=dot:giga; \
 	wget -O go.tgz "$url" --progress=dot:giga; \
@@ -70,17 +78,15 @@ RUN set -eux; \
 	tar -C /usr/local -xzf go.tgz; \
 	rm go.tgz; \
 	\
-	if [ "$arch" = 'src' ]; then \
+	if [ -n "$build" ]; then \
 		savedAptMark="$(apt-mark showmanual)"; \
 		apt-get update; \
 		apt-get install -y --no-install-recommends golang-go; \
 		\
-		goEnv="$(go env | sed -rn -e '/^GO(OS|ARCH|ARM|386)=/s//export \0/p')"; \
-		eval "$goEnv"; \
-		[ -n "$GOOS" ]; \
-		[ -n "$GOARCH" ]; \
 		( \
 			cd /usr/local/go/src; \
+# set GOROOT_BOOTSTRAP + GOHOST* such that we can build Go successfully
+			export GOROOT_BOOTSTRAP="$(go env GOROOT)" GOHOSTOS="$GOOS" GOHOSTARCH="$GOARCH"; \
 			./make.bash; \
 		); \
 		\
diff --git a/versions.json b/versions.json
index e87ab80c..ad7e6d48 100644
--- a/versions.json
+++ b/versions.json
@@ -2,42 +2,84 @@
   "1.15": {
     "arches": {
       "amd64": {
-        "arch": "linux-amd64",
+        "env": {
+          "GOARCH": "amd64",
+          "GOOS": "linux"
+        },
         "sha256": "d3379c32a90fdf9382166f8f48034c459a8cc433730bc9476d39d9082c94583b",
         "url": "https://storage.googleapis.com/golang/go1.15.8.linux-amd64.tar.gz"
       },
+      "arm32v5": {
+        "env": {
+          "GOARCH": "arm",
+          "GOARM": "5",
+          "GOOS": "linux"
+        }
+      },
+      "arm32v6": {
+        "env": {
+          "GOARCH": "arm",
+          "GOARM": "6",
+          "GOOS": "linux"
+        }
+      },
       "arm32v7": {
-        "arch": "linux-armv6l",
+        "env": {
+          "GOARCH": "arm",
+          "GOARM": "7",
+          "GOOS": "linux"
+        },
         "sha256": "708c398cb9e5029cfd5b654370978bf0e797d4d4a71153c06c7378db7e249a53",
         "url": "https://storage.googleapis.com/golang/go1.15.8.linux-armv6l.tar.gz"
       },
       "arm64v8": {
-        "arch": "linux-arm64",
+        "env": {
+          "GOARCH": "arm64",
+          "GOOS": "linux"
+        },
         "sha256": "0e31ea4bf53496b0f0809730520dee98c0ae5c530f3701a19df0ba0a327bf3d2",
         "url": "https://storage.googleapis.com/golang/go1.15.8.linux-arm64.tar.gz"
       },
       "i386": {
-        "arch": "linux-386",
+        "env": {
+          "GO386": "387",
+          "GOARCH": "386",
+          "GOOS": "linux"
+        },
         "sha256": "a0cc9df6d04f89af8396278d171087894a453a03a950b0f60a4ac18b480f758f",
         "url": "https://storage.googleapis.com/golang/go1.15.8.linux-386.tar.gz"
       },
+      "mips64le": {
+        "env": {
+          "GOARCH": "mips64le",
+          "GOOS": "linux"
+        }
+      },
       "ppc64le": {
-        "arch": "linux-ppc64le",
+        "env": {
+          "GOARCH": "ppc64le",
+          "GOOS": "linux"
+        },
         "sha256": "c6ddeab22b23ee33f5e8f06f9667e2092f48dbc6d5db553a66f7fe21da73fbfa",
         "url": "https://storage.googleapis.com/golang/go1.15.8.linux-ppc64le.tar.gz"
       },
       "s390x": {
-        "arch": "linux-s390x",
+        "env": {
+          "GOARCH": "s390x",
+          "GOOS": "linux"
+        },
         "sha256": "ba922f54fe99dee3246705bacbfac27fa88375439025429297aa1e9caf3f2297",
         "url": "https://storage.googleapis.com/golang/go1.15.8.linux-s390x.tar.gz"
       },
       "src": {
-        "arch": "src",
         "sha256": "540c0ab7781084d124991321ed1458e479982de94454a98afab6acadf38497c2",
         "url": "https://storage.googleapis.com/golang/go1.15.8.src.tar.gz"
       },
       "windows-amd64": {
-        "arch": "windows-amd64",
+        "env": {
+          "GOARCH": "amd64",
+          "GOOS": "windows"
+        },
         "sha256": "ef05b7141d3c217fb076f0e27249e144296234df96ead8751c0b76784079df97",
         "url": "https://storage.googleapis.com/golang/go1.15.8.windows-amd64.zip"
       }
@@ -55,42 +97,84 @@
   "1.16": {
     "arches": {
       "amd64": {
-        "arch": "linux-amd64",
+        "env": {
+          "GOARCH": "amd64",
+          "GOOS": "linux"
+        },
         "sha256": "013a489ebb3e24ef3d915abe5b94c3286c070dfe0818d5bca8108f1d6e8440d2",
         "url": "https://storage.googleapis.com/golang/go1.16.linux-amd64.tar.gz"
       },
+      "arm32v5": {
+        "env": {
+          "GOARCH": "arm",
+          "GOARM": "5",
+          "GOOS": "linux"
+        }
+      },
+      "arm32v6": {
+        "env": {
+          "GOARCH": "arm",
+          "GOARM": "6",
+          "GOOS": "linux"
+        }
+      },
       "arm32v7": {
-        "arch": "linux-armv6l",
+        "env": {
+          "GOARCH": "arm",
+          "GOARM": "7",
+          "GOOS": "linux"
+        },
         "sha256": "d1d9404b1dbd77afa2bdc70934e10fbfcf7d785c372efc29462bb7d83d0a32fd",
         "url": "https://storage.googleapis.com/golang/go1.16.linux-armv6l.tar.gz"
       },
       "arm64v8": {
-        "arch": "linux-arm64",
+        "env": {
+          "GOARCH": "arm64",
+          "GOOS": "linux"
+        },
         "sha256": "3770f7eb22d05e25fbee8fb53c2a4e897da043eb83c69b9a14f8d98562cd8098",
         "url": "https://storage.googleapis.com/golang/go1.16.linux-arm64.tar.gz"
       },
       "i386": {
-        "arch": "linux-386",
+        "env": {
+          "GO386": "softfloat",
+          "GOARCH": "386",
+          "GOOS": "linux"
+        },
         "sha256": "ea435a1ac6d497b03e367fdfb74b33e961d813883468080f6e239b3b03bea6aa",
         "url": "https://storage.googleapis.com/golang/go1.16.linux-386.tar.gz"
       },
+      "mips64le": {
+        "env": {
+          "GOARCH": "mips64le",
+          "GOOS": "linux"
+        }
+      },
       "ppc64le": {
-        "arch": "linux-ppc64le",
+        "env": {
+          "GOARCH": "ppc64le",
+          "GOOS": "linux"
+        },
         "sha256": "27a1aaa988e930b7932ce459c8a63ad5b3333b3a06b016d87ff289f2a11aacd6",
         "url": "https://storage.googleapis.com/golang/go1.16.linux-ppc64le.tar.gz"
       },
       "s390x": {
-        "arch": "linux-s390x",
+        "env": {
+          "GOARCH": "s390x",
+          "GOOS": "linux"
+        },
         "sha256": "be4c9e4e2cf058efc4e3eb013a760cb989ddc4362f111950c990d1c63b27ccbe",
         "url": "https://storage.googleapis.com/golang/go1.16.linux-s390x.tar.gz"
       },
       "src": {
-        "arch": "src",
         "sha256": "7688063d55656105898f323d90a79a39c378d86fe89ae192eb3b7fc46347c95a",
         "url": "https://storage.googleapis.com/golang/go1.16.src.tar.gz"
       },
       "windows-amd64": {
-        "arch": "windows-amd64",
+        "env": {
+          "GOARCH": "amd64",
+          "GOOS": "windows"
+        },
         "sha256": "5cc88fa506b3d5c453c54c3ea218fc8dd05d7362ae1de15bb67986b72089ce93",
         "url": "https://storage.googleapis.com/golang/go1.16.windows-amd64.zip"
       }
diff --git a/versions.sh b/versions.sh
index 2773672a..d5f8bee0 100755
--- a/versions.sh
+++ b/versions.sh
@@ -4,7 +4,7 @@ set -Eeuo pipefail
 # see https://golang.org/dl/
 declare -A golangArches=(
 	['amd64']='linux-amd64'
-	['arm32v7']='linux-armv6l'
+	['arm32v7']='linux-armv6l' # the published binaries only support glibc, which translates to Debian, so the "correct" binary for v7 is v6 (TODO find some way to reasonably benchmark the compiler on a proper v7 chip and determine whether recompiling for GOARM=7 is worthwhile)
 	['arm64v8']='linux-arm64'
 	['i386']='linux-386'
 	['ppc64le']='linux-ppc64le'
@@ -97,13 +97,44 @@ for version in "${versions[@]}"; do
 	echo "$version: $fullVersion"
 
 	export fullVersion
-	doc="$(
-		jq -nc '{
+	doc="$(jq -nc '
+		{
 			version: env.fullVersion,
-			arches: {},
+			arches: (
+				[
+					# the full list of *potentially* supported architectures
+					"amd64",
+					"arm32v5",
+					"arm32v6",
+					"arm32v7",
+					"arm64v8",
+					"i386",
+					"mips64le",
+					"ppc64le",
+					"s390x",
+					"windows-amd64"
+				] | map({
+					(.): {
+						env: (
+							{ GOOS: "linux" }
+							+ if startswith("windows-") then
+								{ GOOS: "windows", GOARCH: ltrimstr("windows-") }
+							elif. == "i386" then
+								{ GOARCH: "386", GO386: (if env.rcVersion == "1.15" then "387" else "softfloat" end) }
+							elif . == "arm64v8" then
+								{ GOARCH: "arm64" }
+							elif startswith("arm32v") then
+								{ GOARCH: "arm", GOARM: ltrimstr("arm32v") }
+							else
+								{ GOARCH: . }
+							end
+						),
+					},
+				}) | add
+			),
 			variants: [],
-		}'
-	)"
+		}
+	')"
 
 	arches="$(jq <<<"$allGoVersions" -c '.[env.fullVersion]')"
 
@@ -118,8 +149,7 @@ for version in "${versions[@]}"; do
 			if sha256="$(curl -fsSL "$url.sha256")"; then
 				export bashbrewArch arch url sha256
 				doc="$(
-					jq <<<"$doc" -c '.arches[env.bashbrewArch] = {
-						arch: env.arch,
+					jq <<<"$doc" -c '.arches[env.bashbrewArch] += {
 						url: env.url,
 						sha256: env.sha256,
 					}'