bouncybouncy: There is an option in Settings to sort your next games by time of last move (select Ascending, but not sure)
With this setting, any games that you have just played, and then your opponent comes and plays right back will be left at the bottom of the list, allowing you to play all the other games first. So, worst case scenario, you'll play a move against all your online players before playing a move in every other game, but it will garantee that you make a move in every game before playing in the same game again.

Since the setting doesn't affect the ordering in the main page, if it doesn't seem to work try to switch from ascending to descending...

Hope it helps.