Have you had an evaluation with an occupation therapist?
They may be able to provide some suggestions.
Also, diet could be a factor, like sensitivities to wheat, dairy, etc may not manifest in the form of an allergic reaction, but in these types of behaviors, or may be making them worse.
My son is now 12, was diagnosed ADHD at 7, and exhibiting similar behaviors to those described. I have found that consequences for behaviors we don't want and modifying diet were very helpful.
OT helped give suggestions for school, like he was always tilting his chair back so he had an exercise ball to sit on, being allowed to chew gum so he wouldn't tap on his desk, being allowed to stand up at the back of the class room instead of having to sit still, which required too much concentration to do and he would miss out on the classroom instruction.
Best wishes!