Not sure of your parental situation - ie is there a dad - but you might look at questbridge as a way to enhance your admission opportunities at these schools and more. It changes if there’s more income. Many will count the second parent even if not contributing.
You are obviously very accomplished.
Don’t self study AP. Take the class or let it go.
Do go to your private boarding school counselor. They will likely have a better idea of where a student like yourself gets in than anyone here.
Good luck.