JC and I had a talk about this last weekend...and even though I think it may be too confusing for the NFL to employ, I think this does sort of make sense.
You kickoff just like you would to start NFL overtime now...but both teams have to have a chance to score. Once both teams have had the ball...then whoever has the lead, or takes the lead first wins.
So...Team A gets the ball, scores a TD...then they kick off to team B...who needs a TD to keep the game going, if they don't get it team A wins. If they do get it...they kick off to team B...and then the next team to score any points wins.
If Team A were to go to 4th down, they could punt, or go for it or whatever, and if they punted, then if team B took the ball and scored, then they'd win. Pretty much, once both teams have had the ball it turns into how the NFL is now...but at least both teams had a chance.