Is the public school, perhaps with a gradeskip or some subject accelerations (or both) an option?
Is there a different private school that might be more willing to see things your way?
and
Have you been entirely clear about what the problems you are seeing are, with little vignettes to illustrate your point? You may want to write it all down, and ask them to read what you've written and think about it.
We are all trained to be agreeable and socially accommodating, the challenge of writing down exactly what you see as the problem, not assuming that they see the problem, but spelling it all out, and including a lot of the emotional pain, might help.
Think back to that last time you were on the dating scene. Remember how few people were really able to 'say what they mean and mean what they say.' Based on that perception, realize that it is perfectly fine to pretend this meeting never happened and keep presenting your case over and over and over. Literally become deaf to anything you don't agree with and keep asking. And look into alternatives.
One tip is to schedule meetings at the end of the school day, when the interested parties might be willing to agree to 'anything' just to be able to go home.
Best Wishes,
Grinity
