Your DS sounds a lot like our DS 5. Same sort of weird behavior in same age groupings. His older sis is in a class for HG kids and accelerated. He has not had any testing yet. We have noticed the same sort of behavior as you describe with your son. I have taken him to many different preschools and church groups and we get the same kind of reactions, kicking random objects, running around, kids staring at him or ignoring him. Lots of physical OEs. My mother and law said my husband was the same. They gave him a toy to hold for awhile in the younger grades. My DS has a toy to but he is a very young 5. I don't know if this would work as well at 8.
So an odd thing happened. My brother in law started dating a girl who has two children and her children are also like this. The Boy has the same sort of reactions at school. He was diagnosed with ADD the first year in school then ODD and then they said he has AS this year. He is a good six years ahead in math and his reading and comprehension are off the charts. Her DS is a couple years older that mine in second grade now.
Amazingly our kids can play together just fine, no awkwardness, no fighting, no issues. Also our DS gets along fine with peers from DD7 class who are all HG or higher, especially older boys who are interested in international current events or discussing building hypothetical things. The girl friends kids also get along great with similar peers. So I finally quit trying to put DS 5 in regular social settings or make him fit and found a great woman who has worked with gifted children. She has a very small group of kids a couple times a week for preschool-ish classes and works on following directions and listening skills along with pretty open ended play. We also have him in a martial arts class that is multi-aged with two very good understanding teachers. He has worked toward being better in there, but if a new teacher comes in who doesn't seem to get him its back to the kicking stuff and running around. I am doing this partially because he is going to public school.
He is starting K in the fall in a very short half day program, So wish us luck. Or wish them luck!

Anyway, I told my brother in laws girlfriend that I think her kids are gifted. After meeting more gifted kids she agrees and is planning to move them to another setting next year. In her case I don't think her son has AS or anything else he is just really smart and trying to fit in a hostile environment.
Good luck with your son. If you can find other kids at his level I think that would help a lot. Also I think really intense kids with more noticeable OEs do benefit from sensory or OT techniques like what would be done in OT therapy. I Think this is only helpful when it is done in a non invasive, natural way that is not labeling the child. For example: when he is starting to get anxious we squeeze his hands and put pressure on his shoulders and be a calming presence for him. Sometimes we verbally remind him before we arrive to be calm. And explain exactly what that looks like. Having a toy to squeeze or play with and a book to read if they need to take a step away from the group. Having a toy to share that most boys like can also be a good bridge. It is really hard and I don't think it will ever feel normal unless you find other parents and kids that have HG and PG kids, this helps. Our son seemed to get worse the harder we tried to make him fit with same age peers.
Remember no one knows your child better that you. You are probably the only expert on your child. No body knows! If you don't think he has AS your probably right. Who knows whats normal for a PG child probably not many other people besides you, because you live with one.
Two things I tell my kids when they are feeling out of place; Its not you it them and You are normal for you. If he gets stares and non responses after he tries to tell some boy about his theory on invisibility or whatever. Its non you honey your fine that made perfect sense. They said I'm not normal or this or that is not normal. Its normal for you so your fine. My DD who is older 7 will actually say its not me it them and then go talk to someone else(not out loud). This works better if they have a base of real peers so they have someone else to talk to. DD will also tell people if they say that's so unusual or your so unusual, she says its normal for kids like me. If there are no kids at his level find him adult peers there's nothing wrong with adults or much older kids if that's who he feels comfortable with.
Why do they have to be with kids there own age? We don't only talk to people our own age. PS if any of my kids were in a gym with orange cones, unless they had a book or my phone, the cones would probably be flying if I didn't give them the look in time

. Most of the boys in DDs HG class would probably kick them too depending on who was watching them. I'm not sure why, but Id kind of have an urge to kick them as well, especially if there was no one to talk to and nothing to do. Maybe this is the divergent nature of very creative kids.

A lot of the issues that we have had would be greatly reduced by homeschooling. Unfortunately I can not do that right now. I would love to hear more about your situation. Let us know what happens. He sounds like a wonderful boy.