I share harding and Zman's suspicion that this kind of construction is unlikely to work with a majority voting mechanism. Sorry for the slightly boring opinion there :)
It's interesting on this topic, that we still don't have any functioning kind of coinpool/joinpool setup today. There's some threshold of interactivity complexity that current LN sits under because it sticks resolutely to 2 party relationships, and which coinjoin sits under because it has no cross-block interactivity or game theory assumptions for funds safety, but these more complex ideas sit above and so somehow never get implemented. (In case it wasn't obvious, that whole paragraph is basically my *guess*).