The best idea I had heard so far in regards to having private/Catholic schools in the classes.....
The private/catholic schools should be considered entirely separately from the public schools. The private/catholic schools should then be distributed evenly among 1A to 6A based on their won enrollments, based solely on the comparative sizes of the private/catholic schools themselves.
They should then be combined among the public schools, who are rated separately from 1A to 6A, based on the public schools' comparative enrollments.
The dominance of the Catholic schools wasn't as stark this year as in years past.. but I still am not sure how to make it "fair" when a private school can entice kids to come play football from across an area that encompasses multiple AAAA school districts and then go compete at a a AAA or lower level based on their enrollment (all the while providing reduced tuition for kids who can play football).
I don't think it would make things "fair", but I think it will make it "closer to fair".
For example, a hoops team like Trinity, that competes with other public schools at AA because of enrollment size, may have to shift to AAA or AAAA (using this year's classification system for simplicity), because of their size relative to other private schools.
There is not much that can be done about the top tier private schools that already dominate the upper tiers of AAAA.