What I'm describing is not "gmail" - it's everything that gmail has and offers, but @gentoo.org domain. I'm using it right now in fact.
You get the web interface, IMAP, POP, 2 token authentication (if you want to enabled it) and lots of other things. etc etc It used to be free, but now google charges for it with an exception for non-profits. The admin could test it and see if it provides all the features you need. If you do SSO it may even be possible to integrate with existing infrastructure.. blah blah.. I'd highly recommend someone who actually has to manage this take a look.