Hugs to the OP- your son sounds absolutely fantastic and I know this is a complicated situation to sort out. I think finding an affordable option- even if it’s a college that hadn’t been on the radar earlier- is job 1.
I just want to point out a very common misconception that’s been repeated a few times which is that the “highly rejective” colleges select extroverts over introverts. I don’t believe that’s true, and having gone through several years worth of training, candidate reviews, post-mortem’s etc. from one of those colleges during my years as a volunteer interviewer- it’s definitely not true for Brown.
You do NOT need leadership- it’s just that leadership roles tend to need less explanation than “quieter” pursuits like stamp collecting or reading. You do NOT need to be an extrovert, although I imagine that if you did an analysis, extroverts find it easier to write a compelling personal statement (all things being equal of course- you still need to be a capable writer). You do NOT need to have oodles of volunteer hours, or any of the other things that folks here have posted.
But at some point in the application- either the teacher recommendations, or the guidance counselor summary, or the essay, or the section on activities and awards etc.- something “personal” needs to land. The Adcom’s are accepting a person, not an algorithm of “top scores, top grades, very accomplished” and that personality (whether it’s someone shy, someone outgoing, someone who shuns the spotlight or someone who gravitates towards it) needs to come through in a way that is authentic.
I grit my teeth when I see “the Ivy’s only want leaders and extroverts” because it’s demonstrably not true. Spend an afternoon on any campus and observe, see the posters for the activities going on, pop your head into a sculpture studio or a music practice room, or even head to the rare books library and see the students in their cotton gloves (so they don’t get dirt or oil or even their genetic material on the documents) totally absorbed in their own solitary passion.
The students in Hasty Pudding, Whffenpoofs, or any of the other well known performing arts groups at the Ivy’s? There are introverts there. Not as many as the more outgoing members- but they are there.
OP- congrats to you for raising such an accomplished young man. You guys will figure this out, I think there are a lot of solid suggestions made so far. And a lesson buried here- your son can be the shyest person on the planet, but asking for help is something he can learn to do. He will need that skill in college, and he will need that skill in his future life. I am sad that his guidance counselor wasn’t more proactive in reaching out but that’s water under the bridge.