I say split private/public schools. Have 4 classifications in all sports (instead of 5 for FB and 3 for all other sports) for public, 2 classifications in private.
Then for basketball, I say to get rid of district tournaments all together. Have one big region tournament with all schools from the two districts, with top two advancing to the sectional and sectional winners go to state tournament. For example: say 1 district has 6 teams and 1 has 7 teams. The district with 7 would have a play-in game between #6. The one and two seeds would have byes. #3 from one dist plays #6 from the other dist, the #4's play the #5's. The winners then move on to play the 1's and 2's. Play everything up to semifinals at the higher seed like you do first round of the region now.
Not sure if that example makes sense or not? But 1 big region tourney is my suggestion. And I like the idea of rotating the state, even though I like to go every year too.