I would prefer the old system with conference champs always going to the same bowl games. Have the committee match opponents to those champs to make pairings as fair as possible and have the New Year's Day bowls serve as quarterfinals. Your five champs, your top G5 team and two at-larges slot into four games. Then the semis and final go on as scheduled, if a few days later.
I know the presidents will balk at it because it pushes the season an extra week, but it's only for two teams.
I just miss the Big 8 fans throwing oranges on the field and the Big Ten teams always pointing at the Rose Bowl. If UT can't play A&M, and Pitt can't play West Virginia, etc., at least let the SEC champ go to the Sugar Bowl every year.