You could try Mutants and Masterminds. 95% of the number crunching is front-loaded, as it is a points-based, effects-based system. After that, things run on the d20 model. Runs really smooth, and it really doesn't have as much to keep track of once you're used to the system. And since it is superheroes, I'm sure you can figure out how to do a rotating cast with that.
Alternatively, my gaming group also has board games for times when too many people are missing, or we just don't feel up to running the game that week. Settlers of Catan and Betrayal at House on the Hill are two of the favorites, though games like Munchkin, Three Dragon Ante, and such are popular too. Settlers is a classic game, so you should have someone in the group who knows it already. Betrayal is essentially every horror movie ever made. You wander around a creepy abandoned mansion that is never in the same layout twice, until suddenly someone turns Traitor, and unleashes a masked killer, a giant two-headed snake, demons, or so many other things.