I think this is a good and effective proposal.
If a players times out on more than acertain amount of games, he gets limited in the number of games he can start. There are many possible thresholds, for example:
Tmed out in more than 20 games in 24 h => cannot join tournaments or games for 24 h
Or:
Every time you time out (a single game), you cannot join any other game or tournament until you have no more games where it is your move. - this would force that player to make a move in all games before he can start new ones. Maybe a bit too harsh.
Or:
- after any timeout, you can only start games or join tournaments if the number of games where it is your move is less than the number where it is your opponents move (so you need to move in half of your games)

There is an infinity of other ideas, most anything would do though. Just some limitation would help.