So sorry to read that things aren't so great.
I have a 9 yo son and he's a wriggle worm. He's always in motion and has a hard time sitting. I think he's looking for some kind of sensory input. A friend who has a gifted dd about the same age, also with a problem with wiggling around and not sitting, pressed the school to accommodate her by giving her a specialized cushion to sit on and she finally quit getting notes home about that behavior.
Behaviorwise, bored kids just do that. They know busy work when they see it. They don't care to color a map -- that's for kindergarteners you know. Boring!
Can you approach them about letting him go to a grade ahead for math and/or another subject? If they agree to a trial run, you can see how it goes and maybe be in a better position to advocate for a grade skip. Ask for it as a trial --- three weeks or so with a firm meeting date so you can discuss.
For our DD12, she is now in Alg 1 and they had to accelerate her to an 8th grade math to make her schedule work so she could have the algebra. They want us to grade skip her to 9th next year from 7th this year. But the split classes (half 7th, the 8th grade reading, and the Alg 1 in the high school building) also let us bridge that gap, while giving her a little time to transition because she's meeting some new people while still having some classes with age peers.
Meanwhile, see if you can make friends with teachers who would teach him next year, in case your private school option doesn't pan out.
I can recommend reading "Teaching Gifted Kids in the Regular Classroom" by Susan Winebrenner. I am not a teacher, but I, as a parent, found this book extremely helpful in advocating. I like the testing out of a unit option. Maybe that's something they would consider. If he could consistently pass a pre-test on the material, maybe they'd get the drift and realize they're wasting their time and his on things he already knows.
Good luck! Chin up and keep on fighting the good fight.
