" All classes at school are finalized and now he can only drop something but not add - no exceptions." I find it hard to believe that kids who didn’t get in to some of their classes are not allowed to add after learning this. Did you ask? It might be worth asking higher if the GC says no.
It looks like you are in California from your college list. You can check https://cvc.edu/ for online classes offered through other California community colleges and some privates. However, it’s kind of late to be looking, as I think many CCs started this week.
Stanford Online High School (used to be EPGY) has some a la carte classes at higher levels in math. However, they are also in the “expensive and not fitting his learning style” category. AoPS is less pricey, but still online. Wouldn’t likely be able to get that on his HS transcript, however.
Do you have a local UC campus? Their Extension programs sometimes let HS kids register on the 1st day of classes for anything that still has open spots. Regular UC per unit tuition. The quarter system can be a shock to kids used to long HS semesters, however.
AP Physics C is a good bit of math. (Wish our school would offer it, but that’s another story…) Maybe some tutoring of calculus to keep the details not needed in Physics C fresh?
@NCalRent - well you tried 
@wayneandgarth perhaps I was too subtle.
According to my dictionary -
Catastrophe:
1: A sudden and widespread disaster.
2: a momentous tragic event ranging from extreme misfortune to utter overthrow or ruin
3: A violent usually destructive natural event (as a supernova)
As a parent of one college Jr and one high school Jr, I understand your concern and frustration but, a little perspective goes a long way. Nobody died, no world imploded (or to Supernovas explode?) Catastrophe is a bit over-dramatic. Don’t you think?
Your son has what you feel to be a sub-optimal schedule and it seems to be everyone else’s fault.
What did your son do while he wasn’t in Math class this summer?
Catastrophe: word that got people to open and comment on this thread, as compared to an earlier thread by the OP that got only one reply.
Clickbait: (on the Internet) content, especially that of a sensational or provocative nature, whose main purpose is to attract attention and draw visitors to a particular web page.
I agree that it isn’t a “catastrophe,” but there are various possible solutions, and enough people here have been through and are going through similar situations to be able to provide a variety of suggestions for the OPs son. For a kid planning to major in CS and physics as the OP wrote elsewhere, a year-long math gap is probably not the recommended path.
Supernovas actually collapse (so implode) first when fusion stops and the star no longer produces outward pressure to balance gravity. The outer layers contract rapidly and “bounce” off the inner core of the star, creating the explosion.
My STEM kid exhausted her math options after 11th grade. Took no math senior year. Never gave it a second thought. Went to Yale. Graduated. This is not a catastrophe.
Will the GC still check off that he took the most rigorous course? I’d use that as a definition of “catastrophe” or not 
Why can’t he add a music or art or other course just to have six like his peers. It makes no sense that kids cannot add classes if there is room.
My future economics major kid did not take any math after 11th grade even though there were options available to her. She had completed BC Calculus in 11th grade but did not want to take either multivariate calculus or AP Statistics in 12th grade. Never gave it a second thought. Went to Cornell. Graduated. This is not a catastrophe.
I agree that “catastrophe” is indeed overly dramatic - but that’s how I felt initially writing the post. Probably should have calmed down first, sorry about that.
However, people did give a lot of useful advice and support for which I am very thankful!
S’s summer was pretty quiet. His lack of college work allowed us to take a family vacation (so no complaints there ). The rest of the time he mostly took apart and back together OS on his computer, did a hackaton, organized another one (at home with a few friends), had a lot of fun doing some proofs for math problems with a friend, did a bit of volunteering in the park, read books and (of course!) played Dota while listening to our loud complaints about it. Generally had a good time.
Oh, he also finally did his drivers ed and started his college essays.
Yay! 
Aaah! What a shame! Excuse my spelling in the prev. post.
Their school does many things I don’t understand. Addition of the courses is one of them but they emphasize it from the summer before freshman year and reiterate every year “The last chance to add classes if during the scheduled time 2 days before school starts.” Besides, he wouldn’t want to add any art or music at that point - he was still hoping to get his math.
In my experience, some rules are ironclad and other rules are just hopeful guidelines which are routinely violated. You don’t know until you try. It may well be that they can’t deal with the entire population of kids shuffling schedules at the last minute, but that in your son’s case they would be willing to add a course considering that he didn’t have his schedule finalized by the CC in time to know. Have you asked?
Incidentally, my daughter was unable to schedule a college class she wanted and ended up with 2 study halls for her spring semester of senior year. She decided to use the time to self-study Physics C, which is not offered at our school. It was fine. No catastrophe. If he can’t get a class, just find something to do with the time.