This is just one area where I'm skeptical unless it's severe. Like our pediatrician said, "of course he has mild sensory processing disorder, that's what's called being a 4, 5, & 6 year old!"
LOL, I agree. There are instances when it is severe definitely...but I work with 4 and 5 year olds all day in a school and we use sensory stuff with kids all the time because they need it. Almost everyone has some sensory issues and can benefit. If the movement is really a big problem them get a basket of those items that are good for active kids in general. Like those little twisty things you can play with....called "tangles" I think. And other things like that. I have a basket of these items in my office. Some kids (and adults) just focus better when moving.
It could be ADHD or maybe not. I am not a fan of labelling unless it is going to help with treatment and services. If he is just moving a lot and still able to focus and concentrate and you are willing to homeschool then I don't see the big issue. If he is not growing out of it as he gets older and it is becoming a problem then that is different and you can pursue it. His description is incredible. I have never heard a child describe something like that. I have had some adults with ADHD describe a similar feeling...but usually included with it is the difficulty focusing and paying attention and having to work really hard at it, and having a million thoughts in there head and being unable to sort it out. that is different than his description.