TuffToodle. I don't know what state you are from. In GA there are two options, private and public.

In the public school (DeKalb county) they do discovery day (full day) as soon as you become gifted certified. Most see little value in it. Compacting math (18 month accelerated math in 12 months every year) starting in 6th grade. They have 2 gifted charter schools (Kittredge is one (for all gifted or highly accelerated kids and the rigor and attention feels like a private gifted school. These schools are free, require testing and then a lottery, which serves only about 10% of the need. This allows kids to get to Precalc as a Sophomore and Calc AB/BC + Multivariate. They also allow kids to take an extra 2 courses per year online or other vehicle to get ahead or take up to 2 courses in the summer. Again all for subject level acceleration. By middle school with parent pushing, demonstrated student performance and a lot of nagging to the school and county gifted folks you can get all the acceleration one would desire. I personally have a kid starting at GA Tech this summer as a 14yo and will enter as a Junior. Most public also allow dual enrollment for Junior/Seniors. Other counties don't have these things.

Option 2 is private school. In GA we have been disappointed by most private schools and we have tried many across 4 kids. They have great communication but the kids are generally middle of the road and not the best of the best. They still teach to average with little flexibility to accelerate until Middle/High school. There are a few exceptions of dedicated gifted schools that do accelerate. MIS is one of them, The Dinoff school is another and the one I really love is Fulton Science Academy (FSA). At FSA they allow compacting math starting in 1st grade based on student performance. This gets many to Precalc or Calc as Freshman in high school. They also have many kids grade skipping and accelerating in multiple subjects and will do so at any time during the year. It is 100% fluid. They allow summer school through other programs to come in and leap front a subject to the next grade level. The rigor is really strong and the best I have seen. You pay for this of course.

My advice is to call every private school you have access to driving wise and ask them what they are willing to do and currently do for acceleration. Find those rare gifted private schools that are used to and build around a philosophy of acceleration. They exist but are not often advertising it. These are not the mainstream schools for average kids. Most will require testing to prove some level of competence but off you will go and have no limits.

Some states allow you to go to the public school of choice. Arizona has that rule where you can live in one district but enroll in another one where the school shows better results. You may find a diamond in the ruff in the public school system but it is hard to do and most people pay for private gifted programs.

Sounds like you are beating your head against a wall. I can tell you I have fought a dozen or more times and when you recognize you can't make any more progress you move on. I have moved my kids into multiple schools throughout the elementary, middle and high school years. They have enjoyed the opportunity to meet lots of kids in different environments and were comfortable with that. Some kids need stability. Mine have not. The more flexible and mobile you can be the more opportunity.

Same deal I have found in my career. Moving every 2-4 years has allowed me to jump another level each time. After 1 promotion often companies don't quite see you at the next level as they know you as a single dimension.
Most school principals are the same way. They get burned out and stop wanting to help and bend the rules to push my kiddos after a couple of years. You are the one and only advocate so don't let people stand in your way.

Good luck!