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On the bright side, I was at the school yesterday and spoke with his teacher for a brief moment. She was amazed at his scores, and is now seeing him in a different light, and starting to challenge him. He came home a very happy boy.

That's a good sign and supports your assessment that it's an issue of being under challenged. I ditto the advice to take your time and not get railroaded. When I said I'd take them up on their offer, I thought it was to pay for an IQ test. I'd probably pay for an independent IQ test with a psychologist who specializes in gifted children before deciding whether to go to a pediatric neurologist.