I think you are right. Maybe guarantee the conference champ if they have one or fewer losses, otherwise the top ranked team in the conference. Then one for the non-power conference which would include ND. Two at large would be the highest ranked remaining teams regardless of conference affiliation or lack thereof. Best teams get in, all the conferences represented and conference teams still encouraged to have strong schedule in case they lose conference championship game. So this year that would work out to:
Alabama
Clemson
Notre Dame
Oklahoma
Ohio State
Washington
Georgia
either Michigan or UCF since ND would have filled the requirement non-power conference/independent slot.
In this case, the top teams all get in and the only inequity is Washington getting in over Michigan or UCF and even that is only by a slot. It seems at least this year to cover all the teams with a legitimate shot and would be pretty fair while still servicing the power 5 conferences. It would also encourage the non-power 5 conference teams looking for a shot to schedule strong non conference games since they need to be the highest ranked to get an automatic bid.