Hello again, OP -
Thank you for this further information. Given your constraints, I don't see the point of looking at state schools (the UC schools, Michigan, VA, Texas). I doubt they will have aid for international students. If one of them has a programme that specifically appeals to your DS it is worth investigating, because they are all very large and sometimes you get a wealthy donor with a particular interest. But normally the state schools focus most of their aid on in-state students and certainly on Americans. Sad but reasonable from the perspective of the state taxpayers.
An MIT academic once told me that MIT has a surprisingly good English Department. He said they realised that they need some strength in the Humanities for the undergraduates who realise after arrival that they aren't going to make it in STEM in that ultra-competitive environment. I'm not suggesting that one would set out to study English at MIT, but if it is the secondary interest of your DS and STEM is primary, then given that MIT has good aid for international students and cannot be beat for STEM it seems worth adding to the list. My sense of the place is that students are happy there, although your DS should investigate online forums.
He might also investigate Carnegie-Mellon - superb for CS and very good for some other STEM. I don't know what the aid situation is.
Duke is generally outstanding at the undergraduate level with excellent aid for international students so I would add it to the list. Chicago is not as well known as it should be, IMO. I would say it is up there with Harvard, Princeton and Yale in terms of offering a rigorous, rounded education. Possibly even more demanding. I hope their aid situation is good. Stanford is of course another great choice.
You might also want to consider the elite colleges, such as Amherst and perhaps one or two others (Haverford? It is a men's college with a nearby sister), that offer good aid packages to international students. There is absolutely no stigma attached to an American college. Many parents and students prefer them. The staff usually have excellent academic credentials, but teaching is the primary mission. They interact extensively with students. There is a lot of opportunity for independent study, etc. At the elite universities most of the interaction, certainly in the first two years, is in small groups led by postgraduate students. The big name professors mainly lecture, often at a metaphorical arm's length. The well known colleges, including these two, give excellent preparation for postgraduate study in North America.
I don't know which of these unis want the ACT, which the SAT, and which are making the whole thing optional. Even if optional, I suggest your DS take at least one and get his scores, then send them along if he is happy with them.
Decisions are typically made in the winter or spring, before A levels. Unlike the UK, they are not conditional on final exams. American pupils get grade reports every semester. Those are used in the evaluation of applications.
I think your DS is doing a lot of things right in terms of making American applications: a mix of subjects, the high level extracurriculars (the NGO sounds fascinating) etc. Supracurriculars (independent study in his chosen subject) also help. Would that we still had AS exams! You really need some advice concerning the fact that he won't be submitting semester-by-semester grade reports. Obviously there is a way around this, as British students attend American universities. But I don't know what it is.
BTW, most if not all of these unis should have staff willing to help you. The concern with reaching beyond the Todhunter-Snoots is fairly universal.