Three conventional OT periods, with mandatory two-point conversions for the third OT. If the game is still tied, then it is a field goal shootout!
Kicks start with the ball on the 25 (42 yards) and increase in five-yard increments if both kicks are made. Repeat the distance if both kicks are missed. And repeat until there is a winner. Probabilistically speaking, this is unlikely to go past 57 yards or four periods, but if it does, you start over at the 25 if both 62-yard field goals are missed.
ETA: this is only half-serious.