I hear you, OP. It's hard enough caring for a child with high needs, but doing it with constant sleep deprivation is utter hell!
My first steps would be playing around with routine, room temperature, soft lighting/planetarium, soundscapes (I know he's young, but have you tried different ASMR sounds?) and definitely try a decent weighted blanket.
Does he get plenty of exercise daily? I would aim for him to have more if possible. I assume you've experimented with diet, but I'd keep playing around with that too.
Do you have an autism specialist at your LEA? Or someone within CAMHS? I would also contact your local OT team and ask them for help too.
Do you have a partner or family member who can occupy him for a few hours while you sleep? Sometimes it's a case of relying on different people so as not to overburden any one person (despite the fact you have to do it all the time!) - it's hard to find anyone to commit to regular respite on an informal basis unless you're lucky enough to have a very supportive/understanding network.
Does he have short breaks/direct payments from the council for care support? (not sure what age these start at as mine are teens)
Is there any chance he might have ADHD too? They often occur together and if ADHD is contributing there are likely additional interventions that might help.
You have to keep reminding yourself that as bleak as it feels today, everything will look better once you've had some proper sleep. It really will.
I would also try meditation (for you) - the Simple Habit app is well worth a look. And try to get some exercise yourself as that can really help too.
Has he had a statutory needs assessment from the council? Have you had a statutory carer's assessment?