As a former wrestler, coach, and ref, I always wanted private to be separate. You for sure make valid points with the mediocre private schools. However, those schools are primarily transferred to for academic reasons only. I do not believe for a second that when a top tier wrestler goes to BECHA, Bishop McCort, FCA, etc, its for academics.
Here are my thoughts on how things should be handled based solely off private vs public:
Private and public both have AA and AAA which the only good way I can think of separating is based on enrollment. The numbers would obviously have to be adjusted for private.
Wrestling adopts a football point system. If you earn "x" amount of points in a 2 year cycle, you are forced to move up to the next classification for the next cycle. That goes for private and public. I haven't nailed down if the top AAA public school in a 2 year cycle should move to AA private. Logistics could prove a nightmare.
If a public school has x amount of transfers on their roster that have transferred after 8th grade, they are required to wrestle private.
The state individual tournament would stay as is, private and public together. The team tournament would have 4 classes as mentioned above, and I think you would still be able to do them all the same weekend like they do now.
By no means do I think this is a perfect solution, but I think the basics of this model would be fair and at least a start to resolving a lot of the issues that a lot of fans, parents, and athletes bring up.