The bowl eligibility problem can be resolved by changing bowl elligibilty requirements to only require at least 5 FBS wins, but they must be FBS wins. FCS wins don't count.
Or maybe a rule that if you have at least 4 wins within your own FBS conference, you are also bowl eligible
So if you are playing 11 conference games, and also lose to Notre Dame and finish 5-7 overall you are bowl elligible.