CET: the very best I've ever been at was the Mystic Seaport sing around where there were no turns, and you had to damn well step up (metaphorically speaking if you were sitting down) and sing your song. Everybody who was ready was able to sing

Sounds like my idea of hell. As them as knows me know, I'm a modest and unassertive type until I actually start singing. (I don't think this is particularly unusual - some of the clearest and strongest singers I've heard have been shy and retiring offstage.) So I'm really uncomfortable in "jump in when ready" song sessions, which in my experience often end up being dominated by natural extroverts; in the setup you describe I doubt I would ever be "ready". I might be sitting there with a stash of songs ready to go, but it would take a lot to make me damn well step up.

So turn-taking is my first requirement. Then get a lot of enthusiasts for traditional song in the room, including a few really good singers to give everyone else something to aim for. (Get that right and you won't need to set a quality threshold or make any rules about what people can or can't sing - quality and style will both take care of themselves.) No session-hogging, no egos and not too much chat; firm but friendly MCing. Long ballads, short songs, chorus songs, shanties; some songs everyone knows, some hardly anyone knows. And decent beer.