You could award a Public and Private school champ which would reflect the reality of the system as is without changing a thing.
Eg, last year's 6A "State" champ was Mount Lebanon. The Private School champ was St. Joe's. Give em credit for that. The year before (2020), St. Joe's was the "State" champ or overall champ, Central York was the Public School champ. That is in fact what occurred. Give them trophies to reflect it when necessary,
Your thoughts on a private school opening in Mercer or Beaver County forming potentially a mega power already exists in Mercer County....but in Hoops with Kennedy Catholic dominating the area and often the state with numerous trophies. And....doesn't that already exist in Pittsburgh at Central? But I get your point. It exists in Harrisburg at McDevitt with all the parts in place except the staff to get them over the hump. All else has been in place (close but no cigar) for years. YEARS!