Hi - retired TA with twenty years primary school experience here:
Gosh! I wish I could have met him! (and I like essays, but a few paragraphs makes it easier to read.)
He has to learn that things can't always be perfect (in fact, probably not much is really perfect), and this calling out to amuse other kids is OFTEN what the stupid children do because they can't feel successful any other way, so it is a pity he has to resort to that.
You mention these 'advanced' things he's doing in reading, writing and numeracy, but is he really UNDERSTANDING the content of books, or the relationships in numbers? Maybe you need to test out things like that, and help fill in any gaps or misunderstandings there might be, and then think of ways to move him on to the next level.
Our DS was bright, good concentration etc, and aged 6 he was writing programs for our very primitive computer (this was 25 years ago). He went on to get a degree in Computer Science, and has had several good, and well paid jobs in IT. Now aged 30 he decided he needed a new challenge, and has gone to another university to do a year's Master's degree in Meteorology.
I'm not sure I would agree that bright children don't behave badly, as some can I think because they aren't stretched or stimulated enough, so they get bored and 'play up'.
The more he can do in the way of arts & crafts, construction (Lego, especially Technic, or Meccano, though of course they are expensive) should keep him occupied. Keeping various diaries, say for Nature, recording the weather, doing research and data collection on things like traffic (cars, trucks, buses, bikes etc) doing bar graphs; in the park or a country walk, counting plants, trees, birds, breeds of dog; in town, types of shop, colours of front doors in a residential road. Maybe drawing plans or maps, of your house or garden; his bedroom; the route to school.
Music is good, and you can get keyboards from ÂŁ100 or so; get full-sized keys, and as many as possible, at least 61; don't bother with gimmicky 'teaching lights' etc. It shouldn't be beyond him to teach himself from a good tutor book, with your help, if you don't want to pay for lessons.