I think I posted this idea earlier in this thread, if not it was a similar thread:
change "before they play" to "before they have the opportunity to play". This means that any freestyle game, people still lose points, since they had the opportunity to play once the game started, but the eighth player to play in a quads sequential game would not lose points if eliminated before his/her first turn. Not sure how to adjust the points transfer calculation, but that is still up for debate if this happens.