have you seen/heard about mailpile?
However I am afraid without the opportunity to put a man year work into it, it will be hard to tick all the boxes.
I really hope you succeed, though.
(Disclaimer I am a backer of Mailpile)
Would love a gmail alternative for hosting email on various domains. Look at fastmail - but it's not quite what I want yet.
> Mailpile has a built-in web server and will eventually include a proper web-based interface for searching, reading and composing e-mail.
I'll have to check it out and work out what it actually is/does sometime.