I don't have solutions since there is no easy fix but I can help brainstorm ideas.
It sounds like you have tried class councils--is this when you have a big discussion with your entire class or just students on the council to brainstorm ways to make class better?
1. Can you try having students do restorative circle where they discuss what is it that has been preventing them completing their homework and focusing in class? And come up with a class plan to earn an incentive?
2. I have tried this structure where I put numbers 1-100 on the board with empty spaces. If a student does something well, is kind to another, shows good groupwork, answers a problem and checks in with the teacher (whatever it is that I need them to do) I tell them to go up to the board and pick their "lucky number" and write their name next to it. By the end of the day or week I do a random number drawing. And their names can get chosen. So the more times they do what is expected and get a chance to write their name next to a number, the higher the chance they are at being selected if that makes any sense. I got this idea from
https://functionsarefun.wordpress.co...lucky-lottery/
Good news is just 3-4 more months! Hang in there