I wouldn't require a 2-point conversion after the first OT TD. And I would end OT if there's a defensive score on the first possession.

the game ends once the tie is broken (a safety, pick-6 or fumble return for TD fulfills that). I would prefer 2-point attempts to limit the prospects of another tie and a required 3rd possession, but I would be fine with the normal options being available. I could see value in a just playing a 15 minute period (with 4th quarter timing rules), but I prefer keeping a little of the urgency and excitement of sudden-death.

And I would keep doing it until there is a winner. Hockey isn't afraid to go that long in a playoffs that are at least as grueling. At a very minimum, any other solution can wait until a second overtime period.