If a person wants to quit a game in progress, why not have the resign button like you already have for the other games? To keep it from affecting the game, it could be set up so it wouldn't go into effect until the next round after the current is started. The resigning player would not have their bet count at all in the current round and all players still on the shore could be notified of the player's intention to resign effective the following round knowing that that person couldn't bet in the current round and their score doesn't count either. There is a difference in "No bet, not playing" than betting 0 or 1 to get pushed into the pond.
This won't stop someone from purposely ruining a game, but it will give someone a way out of a game without messing it up too much. Do you think this would work?