Unfortunately, there isn't a magic answer, but I find having very few rules, but zero tolerance of breaking them works. For example, I teach some kids who will call out or interrupt, and although I check them, I genuinely think they struggle to stop themselves. If they're not actually contributing to the discussion, then they're warned that they're out of order. Talking while I'm talking or if someone else is talking, likewise.
We have a two warning system, and they're removed on the third offence, so most are compliant after the first warning. Most of the kids I teach are fine, but I have a few who can be difficult if something has set them off the lesson before. Could you set up this arrangement with your HoD if management won't support you?
For lack of effort, I draw a line along the margin with a highlighter. If they don't get down to the end of the line, it's done in break or lunch. Similarly, if they write rubbish, they can come back and write it again. Be sure to tackle those who sit quietly and do nothing, as well as those who are more vocal.
With my noisy 11s, I find periods of working in total silence is easier to manage than allowing any talk at all. Seating plans and detentions essential. They will get the message.