Don't know much about Marine jrotc
but i do know AF JROTC has an annual honors camp held once year during the summer where maybe 200 or so cadets are accepted.
I recalled while applying to AFJROTC Honors camp that there was a marine one, but i was only eligible for AF- was not accepted (neither my SASI nor I knew if rising sophomores were even allowed).
Ask your JROTC Instructor for the best info. The information website to AF ROTC Honors Camp is partially locked-application parts- to the public- wouldn't be surprised if this was the case for Marines.
Also try looking at STEM at the Naval Academy (for up to rising juniors and younger- I was there this past summer, free of charge upon acceptance, transportation fee not included), AIM at CCA, and the various summer seminars- rising senior year.
STEM=academically oriented but most of us were interested in one or more of the academies (they took a few from each state- 120 per grade group).
app process- simple, list ur grade, accomplishments in EC's, act/psat/act scores, and a few quick essays- paragraph or 2
Since i'm only a rising junior, ur best bet is to ask your child's jrotc instructor