This is precisely https://social.coop, of which I am part of, except for the "not being Mastodon" bit :)

Governance happens on Loomio, which is a forum tailored for community decision making, but the main platform that coop members get access to is a Mastodon instance for now. We are experimenting with Bonfire, which is more flexible and might end up providing a solid base for federated apps in general.

Let me know if you have any questions!