Have you and has he read the Double Degree Dilemma essay by David Lane? It is posted closer to the top of this music forum. The essay really covers several ways to study music- not just double degrees-and it can be helpful for your son (or you) to identify which of the hypothetical young people he most identifies with.
If he wants to major or minor in something else, then he can do a double degree (not double major) at a college or university that has an conservatory or school of music (Oberlin, Lawrence, Bard, Ithaca, U of Michigan, Peabody/John Hopkins, Eastman/U. of Rochester etc.)- or at a college or university that has a double degree program with a conservatory (Harvard or Tufts with NEC for example).
If he does not want a BM degree, but instead wants to do a double major within a BA for music and another subject, that can be fine for a composer. I know students who did not even major in music who nevertheless continued to grad school for composition. (Basically for grad school you need 3-4 good pieces and of course continued summer programs help_.
Most academic, non-conservatory music majors do include composition (and theory and music history). The key is getting pieces played and there are a number of ways to get that accomplished on campus. The other key thing is lessons, which may be with grad students or may be with a professor, may be for credit or not at a BA program, and may or may not have a fee.
If he wants to do a BA double major as opposed to a double degree, he might even want to avoid colleges with schools of music, because some of the best opportunities and teachers go to the BM students. Not always but you need to check that out. At a liberal arts college that does not have a conservatory or school of music, on the other hand, there are no BM students and the BA students can get the best opportunities within the program and also as extracurriculars.
It sounds like your son could thrive with a double degree program- but it is 5 years. Or a double major at an academic BA program. He might want to avoid freestanding conservatories (which he already is avoiding) and also any school where the BM music students would get better opportunities than a kid doing a BA.
In other words, if he is not doing a double degree, he might even want to choose colleges that do NOT have schools of music.
Every school is different so you really have to dig deep. You have already talked to professors and program directors so you are probably getting details that I don’t know about!
ps his teachers and peers must have some good ideas for him- he’s fortunate to be at Brevard; acceptance to their summer program also shows some talent
pps Interview questions vary from a somewhat grueling session at one school to a relaxed chat at another; it’s hard to generalize. He should be ready to discuss his music, mainly.