You do sound very depressed - who wouldn't with so little sleep? - and if you are depressed, you're more likely to want to sleep even more than normal, so this is making your depression worse.
The problem is the rage. It's understandable, it's a physical and emotional reaction to continued sleep deprivation and being continually grabbed at, screamed at and generally being got at when you need sleep. BUT it's also putting you at risk of crossing the line physically with the child. So whether you think it's going to work or not, you're going to have to do something about it other than glare at the expensive books that your child isn't reading.
When he is back, your husband has to take him overnight. You pack yourself off to a Travelodge for two nights. Go there before bedtime so he doesn't wake to find you gone, spend the time sleeping, having very long hot showers, eating in a restaurant, nice food, lots of veg, things that are just for you. Switch your phone off overnight so your husband can't call or message because the child isn't sleeping.
Once you feel vaguely more human again, you'll be in a better place to look at it again.
Is the room dark? Some children are kept awake by nightlights and lights on upstairs. You mention TTLs and ambulances. A proper set of black out curtains will help keep that out. Is your room dark? If not, that could be interfering with his sleep when he does come in. Are you switching on the lights (you mention that) and waking him further/disturbing his sleep/ensuring he's wide awake/stopping him from going back to sleep? Is your husband keeping the lights on when he's taken him and therefore made it a pointless exercise?
You could use noise cancelling headphones or good quality ear filters to wear whilst he takes him for the first half of the night. Just to get a block of three hours, because if you get peace until 10.30pm, you can plan it so you get six hours of not being disturbed before you take over at 1-2am and he then gets his sleep afterwards.
As he usually works from home, perhaps he could adjust the hours he actually works so that he starts a bit later so he could do the night time part until about 4am? That would give you longer to sleep & he'd still get sleep himself. If he's coming into you saying 'he won't sleep, he wants you', that's not happening anymore - the only reason he is allowed to in any way disturb you for that period is if the house is on fire or there is a woman eating Tiger coming up the stairs.
If you see the GP and tell them that you are at breaking point, you might be able to get medication to help you and more help with your child. But they can't help if you decide they can't and never ask them in the first place.
Or, there's the nuclear option where you leave and have 50:50 care. You'll get 3-4 nights of sleep a week that way. If you actually want to, that is - you could choose to be an EOW parent.