Ah, this all sounds very familiar and also became more pronounced following a school move for my DS, now 8. He was 7 when he moved schools. I could have written your post 6 months ago. We went in the opposite direction and have had some success.
We think the behaviour stemmed from an overwhelming sense of being asked to be more grown up before he was ready. With the new school and the move into year 3, there were much higher expectations in terms of independence at school, and I guess we also started placing higher expectations on him at home. I don't think he was ready. We had a chat with him and talked about how sometimes it can all feel way too much when you've got lots of new responsibilities (and freedoms to match) so we were going to help him, because his behaviour at school and home was telling us that he wasn't coping well. Essentially, we removed all responsibility. We started doing everything for him again - calmly and naturally, just like he was 3 again. We went back to helping him clean his teeth, get dressed, get everything ready for school, fully supervising homework, and the like. It sounds tedious, but the extra attention did him wonders. On the downside for him, it meant that he was no longer allowed unsupervised trips to the playground, or to have more grown-up boy freedoms like extended bedtimes. Again, the extra time with him accompanying him to the park, and spending extra time on bedtime stories and routines seemed to help.
We requested a meeting with DS's teacher and we shared our stategy with her and talked about ways she could support the strategy in class. It meant that when he was being disruptive, he was moved to sit next to a teacher before it got out of hand, for example, and he was taken to read quietly indoors if things got out of hand in the playground - all gently, all with compassion for his apparent lack of coping skills.
We had a really good transition into the half term holiday and then an excellent transition back to school. We have been steadily increasing our DS's independence, bit by bit, and scaling back when it seems like he's not coping. We're in a scaling back period at the moment and it seems to be bringing him back again at school and home. We even went back to basics in terms of house rules - being kind, respecting others, telling the truth, and doing as your are told. Each time he 'breaks' one of these house rules, he's sat out from what he's doing for a short time, but close to an adult, and before he goes back to play, etc, we ask him why he was sat out and he explains using the house rules. Again, this has been a helpful strategy at school - the teachers have found it really useful.
Sorry for the long post - I hope it helps and that you and your son can find a solution for all of this, as you say, before he gets labelled at the school for his behaviour. Best wishes!