R.W.
You may have done this, but many schools have financial aid...even for working families. My daughter is in private school and I many children's families receive some sort of help.
There are other schools in the area that specialize in ADHD and some forms of LD. The Shelton School, Fairhill, Oakhill. All are private and expensive, but again, it does not hurt to ask about aid and scholarships.
Good luck, I know this is a hard road.