An option during game setup, that allows a player to use the time remaining on his next turn, to a maximum of twice the limit. I.e. remaining minute may roll over to the next turn of that player.
In effect, a 24 hour turn time limit is then still a 24 hour turn time limit on average. However, it is an incentive to finish one´s turn early, since the time is added to the next turn. So whenever one knows that time will be short the next day, one can hurry up the turn before to make up for the future delay.
Notice that this option actually speeds up gameplay:
I find myself often in this situation: during the week, I have no trouble with a 24 time limit. On Saturday morning it is my turn, I have 24 hours to move. So I make my move, but I do not hit end turn yet, because I know that I will have no time to do my move on Sunday. So even though my turn is fully done, I delay everyone just in case the other happen to be all online and quickly do their turns on that Saturday. Sometimes that happens, sometimes it does not. The only current option to avoid a real stale turn for certain is just to not press the end turn button.
With my suggestion, doing my Saturday turn very quickly, say with 22 hours left, then gives me 46 hours, allowing me to skip Sunday. However, maybe I do find the time and can move on Sunday, so nothing is lost at all. With the current system I cannot do this unless I am certain that I will be able to make my move.