Matthew's high-impact E2E fixes

[lampholder]

I'm a bit worried that (for a change) the big projects might be eclipsing smaller high-impact E2E fixes. Stuff we might also want to consider includes:

• Hunting UISIs; there are still device-list sync issues over federation happening somehow (e.g. Tchap just got bitten by one)
• Ensuring that key share prompts only happen at the right points (rather than repeatedly)

[lampholder]

I split this off from #222 so #222 could fulfil its destiny of being a single issue representing the e2e improvement epic.