A couple years ago, I started some "Turn Blitz" games on PBW...
1 hour turns, 24/7. Game is done in about 2 weeks.
And you have to choose an AI that will work with you instead of against you, since it will be playing half your turns while you sleep
A more structured game, where players submit a turn, and then the game processes 5 times in a row (or some other variation on X turns played for every Y skipped) could be interesting and would be more fair to the players with varying amounts of free time.