Vikings: Ok, i read that 3 times and still don't understand the chain of events you describe so let me try:

6am Tuesday: Turn starts, you move.
9am Tuesday: Everyone finishes, new turn starte.
9am Wednesday: you time out.

So you still get 24 hours on turn 2, just as you would for any other 1 day/move game. If you can't keep up then play the 3 day/move instead.