ADHD and Neverending LOPs

My six year old son seems to have extreme ADHD. He has not been diagnosed, but his 8 year old sister has. It in incredibly hard to get his attention and hold it. He also goes to back brain very quickly. Hiding, panicking, shrieking like he's being injured, out of control sad wailing when he doesn't get to go with Mama to the store, for example. Lots of experiences watching his older sister do many of the same things.

He's very tender-hearted. Very timid to meet new people or go to new places. Very much clings to mama and papa still. But he's also boy and ALL body. Constantly touching others, bumping others, poking us to get our attention, etc. It's often halfway affectionate, but we've taught him continually about body space and he is very slow to learn. Sometimes it's not affectionate. He hits, throws things, screams, etc. We do a modified rule of three with him that earns a 2 hour loss of privileges (LOP). We've been doing TSG consistently for 3 months.

For the last 10 days he's just been in a constant loss of privileges. He'll refuse to get started or start for awhile and then get frustrated about a chore he doesn't like to just start rolling around on the floor and not obeying. He'll get his LOP restarted over and over. We're sending him to school during the day. Great school that gets him. Small class size. We can't keep him at home due to our jobs, but his morning routine tends to go decent anyway, so he's in control when we're heading off to school.

Impossible for you to know with such a brief description, but do you have any thoughts? We're staying consistent and being patient but it's a marathon and so sad to see. We want so much better for him! The family mission is a common topic and we have some goals written out for the kids for different activities that are 'unlocked' as they begin to have consecutive days where they are using their four basic skills. He seems motivated by these, but in the moment he just cognitively can't seem to pull things together, even though he's way ahead of his peers in reading and math.

The ADHD thing and his extreme 'body-ness' are our big question marks right now. Is there any way to help him better? He's so young and it just seems like his emotions are too much for him, but he's also just feeling hurt by the world and is lashing out in ways that are wrong and very unhelpful, even to him, and needs continual corrections.

Thanks for reading!