I've actually wondered why I didn't see people doing this sort of thing. Is there a particular reason you can't right now? It's a little clunky but:
1) Start a thread somewhere, advertising the plan and the time to start, etc, asking for people to sign up for when they're willing to play (sort of like a succession game).
2) Have the host start a game normally, could even be 1-player
3) Distribute connection info to the initial set of players, and get started.
4) When someone needs to leave, do the usual save-manage-players-bit and pull in the next person on the list (probably want to plan those handoffs in advance, but if you have to have a gap for a bit you can control the disabled players' stuff).
5) If the host needs to leave:
a) But they can leave the computer on, just make sure they have the ally-control control node built and the others should be able to keep it going ok.
b) If they have to shut the computer down, or for whatever reason you don't want the slot taken up, save the game, quit, and pick a new host (you'll need to make sure folks are given the right connection info, etc), and continue on your merry destructive way.