Tired mum, I feel for you. I am a single parent to a 7yr old SPD child and he has tremendous energy. I agree with all that LAC has put in her posts.
I live In the UK so places to go are different. I take my son to a play area which has climbing and sliding and ball pool. He is there for 2 hrs at a time and while he is there I get a much needed cuppa and bit of quiet time as he is so engrossed with what he is doing.
I too find people think he is naughty and yes you need a thick skin, other people don't live in your shoes and if they knew what it entails they wouldn't want to.
So you are better than them to start with, give them ten mins in your shoes and I bet they would apologise.
Our days are different some worse than others but my son gets up ready to fight every day like his life depended on it. He will argue black is white.
We use trampoline in doors and "pushing walls" and we have a gym ball which I feel he is dangerous on but he loves it. He rolls about on it on his tummy and watches tv on it while he moves. The dangerous bit is he tries to jump on it from off the settee which then propels him in opposite direction usually ending up with him banging some part of him. He is full of bruises from his inability to notice he has banged himself. Because he is constantly moving he is better in himself.
My saving grace this summer was to find someone to take him out twice a week for six hours each day. They took him where ever he wanted to go, all day on train back and forth or visit parks or museum, his behaviour was better, his energy was less and he was getting the full on 1-2-1 that he craves and I kept my sanity.
Housework can wait, do what is really necessary but don't let yourself get burnt out.