Here's what I'd ry.
Just keep saying 'Yes, I know someone's chucked paper, I'm not bothered who, it's boring' in a monotone as you teach your lesson, every time they start the oooh Billy chucked that! business.
Let them go as normal.
At the end, pick it all up, make a pile & photograph it. Also photograph each student's work from that lesson, if it's not of an appropriate standard.
Print them all out & attach to a letter home to those not working (crap pile, that student's work) explaining that 'whilst your son involves himself in this childish behaviour & makes this level of effort, he is unlikely to '
They will protest furiously next lesson that you didn't warn them that you were going to do this. Shrug & say that they are treating you unfairly - you are preparing lessons, marking their work, working your bum off to get them the grades they need, & don't deserve them playing silly buggers. Their behaviour is BORING & you are bored by it.
Assuming you have at least one supportive colleague, ask them to take the biggest ringleader for a couple of lessons. Rest of class: oh, where's Billy? To which you respond: not in my lesson until he bucks his ideas up. Do not explain or justify further.
Also - & this is REALLY important - send postcards home for all the kids who are working well (effort not attainment), so they know their work is recognised, & don't decide they may just as well join in with the paper chucking etc.
Get Billy on his own & say calmly: 'Do you understand why I don't want you - yes, you - in my lesson?' Fix him with a level gaze & make him squirm. 9 times out of 10 he'll cave & agree that he's being a pain.
You are trying to create the impression that their dickish behaviour is tiresome, but it doesn't actually faze you. However, you are likely to contact home unpredictably out of irritation. Also, you see them as individuals, so you notice who is & isn't behaving as part of the herd.
It becomes a bit uncomfortable & unprofitable to be a knob in your lessons: there's no amusing tantrum or loss of control as payoff, they may be isolated from the lesson or get grief at home, & also, they can quite easily play nicely & it will be recognised.
Oh & document/refer EVERYTHING. SLG will get tired of wading through the paperwork & start supporting you, & worst case scenario, you have evidence that you asked for help & didn't get it when the results come in.
Plus - don't let the bastards grind you down!