<p>I agree that there is absolutely no point in trying to raise the already excellent SAT score.
What may distinguish applicants with perfect SAT in terms of admission may be passion. My S, the non-artistic, unathletic couch potato, exuded love of math from every part of his application, even though he had not taken part in math competitions (by the way, an AMC score of 136 in 8th grade is fabulous; congrats to your son).
Your son is well-balanced and seems very level-headed. Try to follow his lead in looking for ways to support his talents. I do want to note that my S's friends were quite varied in their interests and abilities. The majority, however, were older than he in the first couple of years. The school friends tended to be in the same academic teams or to eat lunch at the same time, at the same spot. He also had a group of friends from summer math camp to whom he was very devoted.</p>