Chaim,
I agree with your position as explained now – take into account all types of income and maybe also major sources of expenses – how many kids in school, in college. Sort of like IRS deductions work.
But this discussion shows how complicated this committee approach is. We do not usually have a town-wide respected beis din who can be trusted to deal with these issues in a way that everyone can trust. School management has obviously lots of vested interests and would not be accepted as dayanim oe even witnesses in a beis din about school issues.
Maybe, our times call for a traditional halachik solution: unlimited competition.
More schools – more options, cheaper salaries, more parents can afford tuition and find a school that works for them.
Then, yeshivos will not be checking your income, and parents will not complain about curriculum. The practical question is how to encourage competition.
FHalakha proposes this: neighbors can restrict you from opening a business in a common yard; Town can limit your ability to open a store that competes with locals. BUT, nobody can restrict you from opening a school.
Note that “school” does not have to be K to 12 to semicha institution, you should be able to open just one class in your basement. This also existed at least in Lita. R Ruderman and R Kamenetsky know each other from their first grade rebbe’s yard. They grew up fine without having a school building.