I think the testing might be helpful but be prepared that even private schools might not care too much about it. I took DS to a neuropsych after a brain injury and we found out he was gifted by accident, basically. In the report he said that DS should be placed in gifted ed or he's at risk for not being successful, and the school completely dismissed everything. The teacher wouldn't differentiate at all. If i had paid for private testing I would have been furious, but luckily it was covered under insurance.