I don’t see why they couldn’t just tweak the college football playoff idea. Give each team the ball at their own 40. Advance 60 yards for a TD or 30 (or whatever your kicker needs) for a field goal. Winner of the coin toss decides who gets to play offense first, loser chooses which goal they want to play toward.
In the case of the Chiefs against the Bills, if the Bills won they toss, they would probably elect to let the Chiefs go first. The Chiefs would start at the 40 and do their best. In this case, they score a touchdown.
OK, next the Bills offense comes out and starts on its own 40, going the other way. If they score a touchdown, the game is tied and goes to a second OT. If they do not, they lose the game.
Just like in college, after the first or perhaps second possession, teams are no longer allowed to kick an extra point after a touchdown, but are forced to go for two.
This would be fair, like the college game, but also involve more real football. In the college OT, the problem is not how they actually run it, but that they let the teams start on the 25-yard line, where a field goal is practically a given. My version, outlined above, would make you earn a FG, too.
"We are not provided with wisdom, we must discover it for ourselves, after a journey through the wilderness which no one else can take for us, an effort which no one can spare us, for our wisdom is the point of view from which we come at last to regard the world." --M. Proust