Raising salaries may not solve the problem. As it is, many working families that pay full or close to full tuition find it hard to pay and spend their lives earning money to pay for, edited schools. They have less time to spend with kids and thus have to rely on schools to do more and more of chinuch. Look also at public school system – generally, “taking care” of teachers lead to an expensive system. Furthermore, giving charity funds to schools makes them even responsive to parents (same as in public schools)
Gemora and later halakha provides a carve out for teachers for unlimited competition – so that prices will be lower and parents could afford it. This does not mean “do not pay teachers well”, it means enable true competition and market – enable many smaller schools that parents can easily switch between, encourage transparency of school budgets and educational outcomes, enable parents to use part of the school program, etc. Maybe the generous donors can leverage their funds to move the system this way either directly or by a voucher-type system where parents direct the funds.
For a simple example, why not parents decide which teachers will get additional funds that are coming from outside schools. This will ensure that good teachers stay and not so good leave voluntarily.