(Thinking out loud, mostly) In the short term, I think we could just go by adding a new flavor if that allows someone to use Evergreen for real. I think we should open gates more, even too much if needed, so that we can gather experience. (Also, at that stage, someone like you is probably even more interesting so you'd be able to understand potential issues and know better how to interact with the Jenkins community and report them.)
Sort of allowing tech debt to accumulate temporarily to go past this stage of the product.
But as R. Tyler Croy was hinting, this probably means we'd need someone to help support that bitbucket flavor, that could be partly you Dominik Bartholdi if you agree (not asking you here for any sort of long term committment here, obviously).