As one of these kids, in Massachusetts, I had my math classes at a desk in the hallway by myself starting in 3rd grade, where I was just given an algebra textbook to read. I reviled the process of math lessons where the teachers just asked me to show the other 3 kids in my quad of desks how to do the lessons... I couldn't understand why they could not just grasp the concepts. It was frustrating for everyone involved, and the solution was worse. By the time I made it to high school I'd learned that: I could read the book and nail the tests, so I never did homework. why bother? Unfortunately they grade homework, I used to skip class because I already knew the material and I didn't want to answer for not doing the homework. I never used the muscles I needed to use for learning, and I was so over it I had trouble participating in the classes that were actually great and I enjoyed. There were AP classes in high school that I never qualified for, and I barely graduated, had to go to summer school every year, so I joined the marines which is probably the only reason the school moved things around so I could graduate.
This was a failure at every level of the education system for me, at a school system with 9/10 ratings. I needed engagement as a young student, I needed to learn and be challenged so I _had_ to study for things, I _had_ to do homework to learn... and by the time the structures where there that supported that I was lost already. There were allusions to a better future, I tested in the 98-99 percentile on the Iowa tests (except in English and spelling, I'm just middle of the bell curve there) so I was fed in Johns Hopkins Center for Talented Youth in 6th grade, but that never was anything more than a weekend at MIT learning about some truly amazing science, but it didn't seem to go anywhere. I'm sure my own discipline problems, apparent from a very young age, didn't help. It was just too easy to understand that the authorities around me where full of it, poke holes in their logic, see what I could get away with, etc... all because I was bored.
You've got quite a task in front of you, raising your son. I didn't find an outlet for this "gift" until I was in college and started writing code for real... self learning is everywhere in computer science and the problems are vast and difficult, there is always something new to learn and I do it voraciously. The other thing that helped immensely was learning to race motorcycles, it's a task that mandates preparation and planning, diligent practice, getting up when you're knocked down, and the amount of brain power you need to devote to it quiets down the inner loop I have that is always going. When I'm on track everything is quiet.
I hope you've got the resources to send your child to private school, I always imagined that path would have had a different outcome for me. My kids are in private (I'm also in CA) now and I've heard parents with older kids (even in school systems like Kentfield) saying the same thing you're saying about treatment of gifted kids.