I don't know that I would pay for more testing if they are not going to look at it, honestly. Does the school even acknowledge the validity of the IAS? If not, again, I wouldn't spend too much time on it if they will not utilize it. Despite all of the wonderful evidence out there (A Nation Deceived and now A Nation Empowered), in our experience, acceleration is tough to advocate for if the school simply doesn't want to do it.
Does your school have an acceleration policy?
FWIW, I believe that others here have cited sources which suggest that poor fit can exacerbate some of the behaviors you describe.
I wish I had more helpful advice, but we are following this thread as our advocacy has been going nowhere fast.
