Welcome! You sound like a great, accomplished person.
A couple of thoughts straight away:
- You're not (yet) late but you're not early either and you need to get going on your process. Application deadlines are mostly Feb 1 and though that may feel somewhat off in the distance it will sneak up on you very quickly. There are essays to write, recommendations to request, zoom interviews to schedule, etc. In fact, register with SAO and Gateway (these are the two common-app platforms) and poke around to get a sense for things.
-Look at the many threads in the Prep School Admissions (http://talk.collegeconfidential.com/prep-school-admissions/) and Prep School Parents sub (http://talk.collegeconfidential.com/prep-school-parents/) that deal with school selection, school list creation, etc.
-Look especially for the “Inexperienced Dad” thread and read through it - tons of great advice about the overall process including how to make a list of schools.
-Think about whether you’re applying to repeat 9th grade (a common thing in the BS world) or entering as a 10th grader.
-You mentioned academic rigor. That’ll be pretty much a given at most of the top, say, 50ish BS and even beyond. So ask yourself, why else do you want to go to BS? What else are you looking for? Size? Rural vs in/near a town? All girls? A particular sport or club that operates at a particularly high level?
-Use boardingschoolreview.com to search based on those criteria, including for schools in NJ
-Create a broad list of schools including some that are highly competitive for entry and others that are less so.
Good luck but get going!