Before changing schools, I would do your due diigence in touring and interviewing staff (and other parents if you can find them) at the public school to make sure it really will meet your son's needs. We live in a similarly ranked school district and it was unlivable for my HG/PG child. They did not meet any individual needs because they could just point to their school rank and stats to prove how awesome they are, therefore the problem is your child, not the environment.
Have you brought up your concerns with the current school and do they have any solutions?