Yes, bump it up to 8 teams. Include the 5 conference champions of the Power-5 conferences, the highest-ranking conference champ from a non-Power-5 conference (if they're ranked in the top 15) and 2 (or 3 if no non-Power-5 conference champ is ranked high enough) at large bids. By those rules, the 8 teams involved this year would likely be:
Clemson
Georgia
Oklahoma
Ohio State
USC
UCF
Alabama
Wisconsin
Plus, no team that would miss the cut (even Miami and Auburn) has a realistic case to be above Alabama or Wisconsin for an at-large bid. Zero controversy, and from then on, the champion is decided where it always should be: on the field. Going up 6 teams (the Power-5 conference champions and 1 at large bid, with the 2 highest ranked teams getting first round byes) is also acceptable, but IMO not the best option.