What the friends with whom I've played this and I discovered was that having to play the debate game to determine turn order after every single turn totally gutted the pacing of the match. We were about done after three of them, and ended up hitting randomize pretty much ever since.

So here's the proposal:

Since turns are thematically grouped in threes already, each three being a single school day with morning, lunch, and evening, why not have turn order determination take place each morning instead of every single turn? You determine turn order in the morning, play through morning, lunch, and evening, then determine turn order again the next morning. It's a fun parlour game, but currently is not spaced out enough, and ends up cloying very quickly.

In the, to me, seemingly unlikely event that there are people who don't actually find it a massive pace-killer to play the debate game on voice every 30-40s, and nine or ten times or however many it is during the course of one match, you could have turn order mode be one of the options in advanced settings when hosting a match.