My one child applied to 4 schools that participated in FairTest, did not send his test scores, and was accepted to them all. I had my doubts but 4 out of 4, is pretty good. You will lose out on any merit that includes test scores as part of the reason for the scholarship.
I agree OP should consider some of those schools that do not require test scores.
The other thing he should do is start looking at transfer acceptances at schools. uSC does accept a goodly number. Don’t know about MIT and Stanford. Far less , Im sure. But there are many selective schools that are very transfer friendly. Instead of banging your head against this test score wall, work on getting yourself very well situated at a college that will take you, plan on taking courses similar to the programs that interest you in the more selective schools and work to get straight A’s in those courses so you stand a good chance of transferring. Test scores aren’t as important for transfers. Getting those grades in key courses at college is very important.
This allows you to make a plan and have more positive energy in going forward.