I am not familiar with the specific summer courses and can’t comment on them. Also I can only give my opinion, and I understand that some people may have other opinions.
I do have some experience with a high school student who studied for an AP test on her own, and had some trouble finding a location that would let her take the test. This was however in languages, where the test taking has to include audio equipment. I am not sure whether there would be an issue for other tests. Also, after a lot of asking she was able to take the test (and did very well).
To me computer science seems like a good one for two reasons: Because you seem to be good at it (based on what you have said), and because math and CS are pretty much IMHO the core of STEM, and you already have plans to take AP math next year. I may be biased since math was my favorite subject, and CS was my next favorite.
I am not personally convinced that you need to take more than this one. IMHO taking one and getting a 5 is better than taking two and getting two 4’s. You also appear to be making major progress in your other grades.
I do get your argument that if you can do well on the chemistry AP test, then it would make the point that you poor grade in chemistry is due to a temporary illness, and not due to any inability in the subject. However, I would be careful not to try to do too much.
I think that humanities is more difficult to learn without a classroom (and a live teacher and a class discussion), and this does not look like it is your main focus right now. I wouldn’t worry about it.
I will admit that I have a general philosophy / belief that the US puts way too much pressure and stress on our high school students. There is a LOT of anxiety related illness in US high schools. I believe that our system is seriously broken, and that the “big name” university admission policies contribute to this in a major way. I think that parents and students should push back on this and find what works for us. I do understand that this might mean not intending to go to MIT or Stanford for undergrad, but a strong student does not need to go to MIT or Stanford or Harvard to do very well in STEM fields.
Also, congratulations on your recovery from your stress-related issues. Your good health is key, and it sounds like if you take things at a pace that makes sense for you then you will do very well.