SOunds not dissimilar from my ds (4 in June). He's youngest of 3, reading fluently (ORT4), socially immature. He can share, but on his terms, so has been hitting out a bit, and has refused point blank to do some of the activities, particularly PE changing.
My ds has hearing problems which makes it hard for him, and if I talk to ENT they say his behaviour is typical however I feel he shouldn't be excused on this and they have to treat incidents with consequences. He has time out both at home and at school (I'm not punishing him for incidents at school, just saying we agreed to be consistant for both)
I don't think being at school full time from the start has helped.
What is helping him, is he has a book where they give him a face for every activity. So it might start of the day with "Carpet time good 
; Activities ok 
; playtime pushed other child; said sorry 
"
Then in the evening we can talk them through and I praise the good times, and discuss what he could do better for the bad times. Sometimes he explains what has happened (eg "I asked them not to move the car, and they did so I hit them and they stopped"
) so then I can point out that hitting them was not a good move and suggest maybe telling the teacher, or using another car etc. Often he hasn't got a reason that he can articulate.
It's also helpful because we can see flash points. Typically afternoons are worse (he's tired). Playtime/lunch times can be a problem (apparently this is typical of hearing problems due to the amount of noise). And PE lessons (haven't got a good reason out of him).
Other things have come up, such as last week there was one day he was terrible, worst day yet, and it turned out he had bad ringing in the ear (said a scary noise was following him).
Today he was Star of the Day (which I slightly had to grit my teeth as my older 2 would have been far further down that order due to always being good) but I've praised him to the skies and he's really proud of himself. Only thing is that often a really good day is averaged out by the next day, so I live in fear and trembling of tomorrow. 
Personally I'd like to be able to separate out his hearing issues, just plain naughty/pushing boundries and any other issues. In reality that isn't easy.