The quantum shenanigans would be difficult to do, yeah. It would probably involve some minor bastardyness.
So what I think would be the rough outline for the game:
1) There are no days and nights. That would either imply the existence of windows (bad for keeping people trapped) or knowledge of the current time (yeah no). Instead, there's three phases per round.
2) First phase lasts 24h. No extensions. Everybody is assigned a colour and potentially a partner if they're in a pair. The players can talk to each other and vote on the 3-player groups for the next phase.
3) Second phase, 24h, no extensions. The thread gets locked and every group gets a quicktopic thread for their own discussions. This is when people are behind the doors solving puzzles and shit.
4) Third phase, 24h, extensions allowed. Thread gets reopened again, people can discuss what happened during the previous phase. Pairs get a new quicktopic thread to discuss their vote. At the end of this phase, people gain or lose points depending on their votes, and the first phase of the next round begins. If nobody within a certain group votes, they all die.
5) Some people get special roles/abilities, naturally. E.g. voting before their partner has a chance to pipe in. Yes, dickishness is an ability :V
6) Once somebody has the necessary 9 points, they can choose to end the game, but they can also keep it going for whatever reason. Of course, considering the people here *coughwubacough* precautions must be taken to avoid the "play until everybody can leave" trick.