I agree that I would start by asking if they are open to looking at the results from private testing.

Our school tried to help with subject acceleration after they tested DS (after months of him complaining and getting into trouble). They moved him ahead 2 years in math and science, which academically was where he needed to be, but it was a social disaster that the school was not prepared for.

We wound up pulling him out of school last week, and preparing to homeschool for 3rd grade in the fall. DS was simply miserable at school.