Just play the whole 1/4 in playoffs. Keep doing that until one team wins. It’s a brutal sport, so be it.
That's pretty much what they do in soccer, they play a 30-minutes of Extra Time. Although they stop after the 30 minutes. They had a "Golden Goal" for awhile where the game would end on the first goal, but they got rid of it. LOL, maybe after the first OT they can just have the kickers kick 5 Field Goals.