For us, the best way to advocate for acceleration was with out-of-level testing. Can you ask that the receiving school test him at a level higher than his current grade level? Out-of-level testing is usually done using a test that is 1-2 years ahead of the child.

My other suggestion would be to ask the school to use the Iowa Acceleration Scale to determine his readiness to skip a grade. This is done by you and the academic staff as a team, but does require scored tests to get a complete score.