Expand the CFP to 8, the 5 power conference winners and 3 at-large selections. Win and you’re in. Then pick 3 at-large from the G5, ND, and conference runner ups. This year this would allow Cincinnati a berth, if they win out. Yes, a G5 team almost needs to be undefeated but they will then work on better OOC games against better P5 teams. Even if you have to go on the road. Miami and FSU had to do that as Independents back in the day.
Anything with votes will error. There will still be controversial choices of the 3 at-large teams I provided above, but you can have rules like a guaranteed berth for one G5 team if ranked high enough; only one at-large berth per conference, to prevent the $EC from stacking the deck.