Now that becomes tricky. Lets say that was the rule right now. Bills get the ball back and score. You realistically have to go for 2 because you can't risk giving the ball back to the Chiefs and the entire game comes down to that.
Imo: Each team gets one possession to score. If both teams score it goes to a Hockey Shootout type. Start at the 2 yard line and see who scores (only one play) and these stats don't count towards TDs or anything. Move it two yards after every successful conversion.
So:
Chiefs have the ball at the 2: score
Bills have the ball at the 2: score
Chiefs now have the ball at the 4
I honestly think it's the only way it's fair