Make teams score touchdowns and go for 2. Remove field goals and PATs. Done.
I actually like allowing PATs at first. That way, in the instances where both teams score TDs on their first possession, the second team has the opportunity to decide whether to try for the tie with a PAT or the win with a two-point conversion. I also like the idea of not having OT be basically a field goal kicking contest...
Take the following scenario:
Team A goes out, gets two first downs, fails to score a TD from there, and then kicks a field goal.
Team B goes out, has a two-yard run, gives up a five-yard sack, throws an incomplete pass, and faces a fourth down play.
Under the current rules, Team B is now facing just a 35-yard field goal attempt for the tie and lose only if they miss.
Under my scenario, Team B is now facing a 52-yard Hail Mary play for the win and lose if they fail.
ETA:
Under the current setup, the Defense basically has to force a turnover in order to win the game for their team. Under my scenario, the Defense can basically win the game for their team early in overtime by simply preventing a first-down conversion.