You are definitely in range, but you know, especially as an Asian male with STEM background, Princeton is going to be a high reach; I think SCEA makes sense if it is your number 1 choice, especially if you would be happy at UT as a fall back. (You should also have a decent chance at Rice in RD, so it might not come to that.)
For context, my non-Asian kid with 10 on AIME (4x AIME qualifier, but just missed USAMO), identical SATs, also number 1 but at a private school, more advanced math and APs but somewhat lesser ECs, was accepted Princeton RD in this past cycle (also a few other schools on your reach list, but also turned down or waitlisted at a few).
Looking back on the results, I feel the essays made a big difference. The Princeton application really lends itself to “customization” and if I could offer any other advice it would be to highlight any service opportunities that you have engaged in, and try to have the recommendations tie into those if possible.
Congratulations on a tremendous record, and btw Rice was also a favorite at our house (but did not apply because of a different R/SCEA acceptance).