They should go back to a multiplier for private schools, but instead of 1.35 it should change every year based on overall athletic success across all private schools.
Take the total number of State Championships won by private schools in a fiscal year and divide it by the total number of expected State Championships won by private schools across all classes in all sports. For example, if Class 3 Boys Golf has 70 teams and 7 of them are private schools, the expected number of State Championships won yearly in this classification in this sport would be 0.1 state championships.
This would be for athletics only as high performance by private schools in academic competitions such as quiz bowl would be expected and it doesn't seem fair to punish an academically sound private school like Thomas Jefferson or College Heights for having success in this every year.
For the sake of simple math, I will use more rounded, arbitrary numbers here whereas the actual numbers would probably need to be rounded to the nearest hundredth or so. Let's say that in year 1 of this experiment, private schools won 21 championships out of an expected 10 championships.
21/10 = 2.1
Therefore the multiplier for the next year would be 2.1 for private schools.
In year two, it's harder for private schools so they only win 14 out of an expected 10 state championships.
14/10 = 1.4
Now, you take the 1.4 and multiply it by the existing 2.1 and get your new multiplier of 2.94
In year three, it's even harder with the new multiplier and private schools only win 11 out of an expected 10 championships
11/10 = 1.1
1.1*2.94 = 3.23 (rounded)
In year four, private schools only win 9 out of an expected 10 championships.
9/10 = 0.9
0.9*3.23 = 2.91 (rounded)
The multiplier now goes back down to balance things out for the next year.
Using a method such as this, one of two things will eventually happen and it's a win-win situation:
A. We reach an equilibrium point as indicated above where private schools can fairly compete against public schools.
B. The largest private schools (Metro Catholic 5 + Rockhurst) collectively outpace the expected number of state championships each year because they have nowhere "up" to go in terms of classification. This pushes the multiplier up to 50 and McAuley Catholic (39*50 = 1950) is now competing against Charles Lindbergh (1751) in Class 5 Basketball after Class 6 becomes the 32 largest private schools. We could continue like this or it could force the hand of the private schools and they could eventually reorganize on their own.