FWIW my kid got into UCB, L&S CS major intent with almost exactly the same background - 3.7UW GPA (4.05 UC GPA) 1540 SAT, 10 AP classes, and one of his big hooks was that he also is a candidate master in chess (represented the US at the World Youth before) but focuses mostly on teaching chess and running tournaments nowadays (makes good money at it). I’m somewhat convinced that the chess was what got him in.
I think your chances would be pretty good if you apply for the L&S CS rather than EECS at Berkeley. EECS admittance rates are ultra-low and to a large degree, the 2 programs are the same (or can be made the same).
Carnegie Mellon, you should ED there if you can. They love good chess players and kids who are brilliant at math.