I do feel for you. However, I think you should be more firm yourself.
My DB was in a small secondary school, and his year group boys didn't like studying at all. DB was always with them, they just played on the street all the time. My mum was very strict with him, tried very hard to keep him at home to finish homework first. I still remember the tense between them, as they quarrelled a lot. However, DB was the only one who went to University in that group in the end , and he is now a head of department of a small company.
From your other post, that his school is an outstanding one, I think you should try to make it work first. I would assume, school actually has set homework, but your DS just not care to write it down and do it. Will you be able to get in touch of his teachers to find out the homework? And make sure your DS do the homework. If he doens't do it, you can punish him yourself, like stop him playing his favorite games, stop him going out to play, etc, anything he care about? For all the punishment he receive from school, you should reinforce at home as well. As exclusion doesn't work on him, maybe even sounds a treat for him, as he doesn't need to do any work if exluded. Can you set up some punishment at home that will work on him?
I think you need to really make him to know those behaviours are not acceptable. You can't just rely on school to sovle the problem.If you can't make sure about this, even change school, he will find the naughty students, and form another trouble group.