Every time a game goes into OT (college or NFL) I think of the best OT system possible and come to the same conclusion: just keep playing.
Down, distance and field positioned were all earned by the two teams. Each had an arbitrary kickoff (beginning of game and half). You will get more strategic plays at the end of regulation but there will still be the occasional Hail Mary when a team is down by 4-7 or 1-7 but outside of FG range. Sometimes it will favor the team with the ball at the end but sometimes it will favor the defense (regulation ends 3rd and 14 from your own 11 yard line). It is simpler. It is fair. And often times, OT will end with only one or two plays. Just treat it like the end of a quarter and switch direction rather than treating it like the end of a half.