So, since more signups seems unlikely at this point, I've combed over my thoughts, and decided that a game of Assassin's would fit the bill. This is a variation of mafia, in that there is still a "town" and "anti-town" faction, lynches occur, but it is a night-less game. It is well balanced for six players, which we appear to have.
The setup is as follows. one person is the king, one person is an assassin trying to kill the king. The other four players are guards. The guards know who the king is, but not who each other are. The king and the assassin don't know who anyone is. Each day, someone is lynched. If a guard is lynched, then the next day starts immediately, and repeats. If (Somehow, I wouldn't mention it unless I saw it happen due to someone being very dumb IMO) the king is lynched, then the assassin wins. If the assassin is lynched, then they get to immediately decide who to kill. If they kill the king, the assassin wins, if they kill a guard, the guards and the king all win.
If this is something you are still interested in, please post back here confirming as much. If all six are in still, I'll go ahead and run that game, else, I'll be putting a pin in this due to lack of interest.
Tagging so you get notified to read this. @Eva @HJFudge @JNewhall @Maylan @Flimbo @0zymandius