87% is about a 3.4, not a 3.2. (90= 3.7, 84= 3.0) In addition, since it’s a competitive boarding school, you’ll get a little pass on that due to the rigor in grading there.
Your SAT score will be a bigger roadblock. Try the ACT and take several SAT Subjects (since your boarding school preparation should allow you to get high scores in those, to mitigate the SAT Reasoning scores).
With reaches, odds are against you. Keep that in mind when you apply to your top schools, have good matches and safeties, and you’ll be fine.