Been thinking about you and your little man.
Doc's surely a very long way down the line - there are lots more things to try before we start doing things like that. . .
He's very little to be "chopped and changed" imo. He's likely to be unsettled by simple things at this age, like changing working group, moving up a level in reading or sitting with someone different. Big changes like teachers, classroom assistants or environments can be much harder to cope with.
Here are some things I thought of - both as a teacher and as as a mum. No offence or patronising intended, just some ideas, that I'm sure you're doing already.
Praise the good behaviour, however small. No big deal, just "well done, X, thanks for that, or "good lad, thanks for sitting nicely. Ignore as much of the behaviour that you don't like as you possibly can! Reward chart in place with school will definitely help that.
Can he tell you why he's playing up? Maybe there's something the school has missed - it's sometimes easily done in a busy classroom. Does he feel that he needs more help and this is his way of trying to tell everyone. Maybe one of the other kids is really winding him up. He might be able to articulate what's going on in his head. Ask him how he feels when he's misbehaving and getting told off. Might give some clues?
Make sure that you reassure him that it's the behaviour that you dislike, not him. I've seen little ones his age get in such a state once they start playing up cos they think they can't stop, cos they've blown it with mummy and daddy and everyone hates them now anyway. Obviously not the case, but doesn't hurt to remind them. He should be old enough to understand the difference between himself and his behaviour as two seperate things.
Don't know if any of these ideas might help? As I said at the start, don;t want to patronise you, just want to help.