Anna asks a pertinent question: But without a denomination, how do you get ordained so you can do weddings etc.?
As it happens, Georgia has a very liberal law (yes!) with regard to marriage officiation. Whomever a "religious society" permits to solemnize marriage may; neither the UUA or any other association of congregationally- or independently-governed congregations matter to the state. I deferred my ordination and for two years I was "under licence" from the church that called and eventually ordained me.
But wedding officiation isn't really the point, is it? (After all, over the border in South Carolina, notaries public can solemnize marriage.) UUs get so hopped up on the regular and congregational authorization of temporal authority (i.e. the Board) that we often miss the point when it comes to spiritual authority (i.e. pastors, and where found, deacons). If churches worried about the latter more, and then saw the UUA as a resource (rather than a paper bishop) we'd all be in a better place.
So my question to Anna: in your fantasy church, what is the role of the (lay) pastorate?