He might do better with another sport like soccer. My oldest loved soccer. My youngest hated all of what he calls "sportsball". Meaning any sport where you "pointlessly chase a ball around". For a few years he thought basketball was interesting, but then he learned you had to play it with other people, and other little boys are not so nice to you when you have sensory issues and are not very tall or talented.
One thing I learned from the Occupational Therapist (OT) that we saw is that your son will lead you to the activities that he needs in his sensory diet. He will show you the types of activities he needs. If you get that "Out of Sync Child Has Fun" book that I have suggested, and do the various activities, taking notes as to what he likes and hates, the ones he really likes are what he NEEDS, and what he truly HATES are what he should stay away from. It seems so stupidly common sense, but that is what will help him develop, and will help him stay calm.
One thing that many kids find helpful, esp at your son's age, is a one liter or 1.25 liter bottle washed and dried and filled with rice, small beads, buttons and other small objects. Interesting things that your son might find cool. Found objects, whatever is interesting and can fit inside. Leave enough room for the contents to shift so new things can be revealed and hidden. Seal it tightly and close it with some superglue so it cannot be opened by your son and spilled. Then take it with you to waiting rooms and appointments or places where you might need him to sit and be somewhat still for a little while. he can shake it and find new things in it and old favorites and see what all he can discover. It can be shaken to make a rattling noise if that is comforting to him, but chances are it won't be too noisy. Seeing all the different things in it can be used as story prompts to help you and your son tell stories or write stories to help develop his writing skills too - even if he cannot write well, it helps with his creativity. It might be something he likes.
Given the love for running and crashing into things, he might like a 'crash pad'. You take a twin sheet and fold it in half and sew it up on the long sides. Fill it with old pillows, blankets, anything soft you have, and sew the short side shut. Then he can jump onto it. he can nap on it (if he naps), watch tv on it, whatever. I used out of season bedding and just basted it shut so I could rotate the bedding as needed. It was one of his favorite things, especially for jumping off of the furniture. He was going to jump off of the furniture anyway, this way he was less likely to get hurt. Being the 3rd kid, he wasn't going to get sympathy if he got hurt, so he liked having padding, lol! By the 3rd kid, Moms don't give out a lot of sympathy if the kid is doing something like jumping off of something they should not be jumping off of, Know what I mean?? I think the first kid burns that out of us.
What kinds of things does your son like to do to express his sensory needs?
I am VERY glad you are getting in to see an Occupational Therapist (OT). I totally understand the long drive. It isn't a lot of fun, but I have been there. I hope it is helpful.