Putting games on the back burner

Putting a game you do want to move in right now on the back burner: to stop it automatically coming up after each time you move in other games?

I know some players would use it to avoid defeat and drag out games.

But there are times when you know a game is at a critical stage and you are not your most alert so you wish to save the move in that game for later.

or

Your opponent is demanding you resign, give up or otherwise writing stuff you can't tolerate and you just wish to play in peace.

To click "my games" each time to avoid this is labourious.
Normal timeout/timebanks would still apply.

I know the feeling, what I've been thinking of doing is archiving the game and checking my archives with the 'my move' filter on.