Oh God Show My Homework. Show my fucking homework. That is bringing back some awful memories 
I too had a DC using SMW and with SN (a different one but the same problem of having to micro manage constantly).
Hopefully it will give you some hope to know that my DC got a lot better around 15ish - and I think a lot of it was gaining the maturity to know they had to put the effort in as exams were coming closer so they need to put effort in to do what they wanted to do when they finished school. Plus they realised their mum constantly on their case was a. Annoying as fuck and b. Made them look immature.
So a lot of it was just age and gaining maturity. But in the meantime we worked at it (with the school who had dealt with it a lot!) What is your relationship with the school as ideally they would work together with you to address this (I don't mean them parenting for you but supporting you to parent him to get this better) Does he have any additional support like a LSA/TA? Or an EHCP?
In my case, my DC couldn't have after school detentions due to their SN which didn't help. We tried to find something that was either a good deterrent (loss of pocket money, loss of gaming time etc) but it ended up in more stress and got into a negative cycle and didn't work so well.
So we tried a good incentive and that worked much better. The incentive of course will be different with DC - we gave a later bedtime if they had spent time that evening working - we put extra money on the online school thing to buy treats as well as meals as they would be hungry from all the work
These sorts of things. Also, school got them involved with coaching younger DC in the sport they really enjoyed and I think this helped them grow up and be a better role model.
I tried to remember that their SN also made it harder for them and that should be recognised as well. It's so easy to get into a negative cycle with what they don't do.
I really remember the have you done have you done have you done stage but hopefully it will comfort you to know it should get better as he gets older and all the work you put in will pay off. Definitely worth working with the school if possible.