How about this. The first team to six points in OT wins. A touchdown should end the game as it gives the defense ample chance to stop the offense (unlike a FG.)
Also, imagine the decisions that this would create. A team 4th and 2 on the 35 would have to debate on whether to go for it or kick the field goal, hope for a stop and kick another one. It seems like a way to reward good offense, good defense, and good special teams.
This seems like the proper compromise.