One of the issues here seems to be that you are severely uncalibrated. a kid who has the ability to make USAJMO is not “average” in math. But I think you’re going about this in the wrong way. You’re worried about how to make the kid fit the school. You have an intelligent, hard-working, talented kid. The very best thing he can do is pursue activities that he is honestly passionate about (real passion, not “passion for college applications”). And by pursue, I mean all of in the school context and out of the school context, and most importantly in the summer, when he can hang out with other kids who have that passion as well. (That’s why math camps are wonderful – not as a resume line, but as a place to spend time with “your people” and find out who you are away from the context of your family.) Then you take the kid you have and help him try to figure out where he’ll be happiest for 4 years. That’s it. Nothing more.