Here's another solution: Great for Bowls and Playoffs
Have a 16 team playoff that starts the 2nd weekend in December (the 1st weekend is for conference championships.) Every conference champ gets an automatic bid just like college basketball. That leaves 4 or 5 at large bids. Oklahoma would have gotten an at-large bid this year. Then a selection committee seeds the teams. The first playoff round is played at the higher seed's home stadium. Skip a week for finals. The 8 losers go to lesser bowls (an early upset would land Oklahoma in a lesser Bowl) while the 8 winners go to the big bowls. The 8 winners are still playing out the bracket in the Bowl setting. This begins the last weekend in December and extends into the 2nd weekend in January. The Bowls bid for the rights each year for a particular game.