Perhaps pick a target turn. If you prefer an average of 10 turns per game, roll at the end of turn 9, a score of 5+ ends the turn. Same on turn 10. If the game gets to turn 11 definitely end the game. You might even play turn 11 with rules for fighting in twilight. Though throwing in rules changes at the end of a game sounds like a bad idea. Never mind.
This too shall pass