Re-reading this thread and a couple of additional thoughts:
11th grade is a tough entry point. As much as you may have grown or have new perspectives, it seems a stretch to see you getting in now when you didn’t in the two easier entry points. You’re still you, and that you wasn’t compelling enough to tip luck in your favor the first two times. You’d have to be a different you to have a different outcome, I would think.
11th grade at these schools is traditionally REALLY hard for even the kids who got in as freshmen. The Boarding School experience you seek is a more difficult transition that I think you appreciate. So that it’s already really hard plus the transition may have detrimental implications for applying for the next step, which would be a shame after establishing a presumably great record and reputation at your current school. I find it hard to believe that you just drop in at 11th grade at Exeter and maintain the same trajectory. Would you consider reclassing to tenth (if such a thing happens at these places)?
Many believe that doing great at a great LPS gives you better admissions outcomes than being in the middle of the pack (at best) at Exeter. Maybe tell us why it’s worth it to you.