I can't imagine what it must be like living in this situation and being as dependant on this person as you are. It's absolutely NOT too much to ask for a hug from your partner even when things are good, let alone when things are falling apart for you.
It sounds like there might be quite a lot of bite in the "supporter fatigue" comment (which is not any kind of judgment on you- a hug isn't much to ask for). If that's what's going on, then it makes a bit of sense that when things are fine for you, they're fine for him, but whenever he's confronted with "I like some help now", his brain goes into meltdown "I've got nothing left to give" panic and horribleness directed at you.
Just a suggestion, but what if you recruited him to help you get some more independence, like tracking down a birth certificate, getting ID and a transport pass.
Apart from placing you in a better position if things reach breaking point, you could tell him up front - "My illness seems to be a bit much for you to manage right now, so if you can help me organise transport, meds, banking etc on my own, that will take some of the load off you..."
In the meantime, the only thing worse than needing a hug and not getting one, is going to the length of actually asking for one and getting knocked back. You guys had a plan that he'd do that, but the plan isn't working, it's making things worse...at the moment. Maybe temporarily try and use other self-soothing strategies that don't mean relying on someone who, at the moment, can only be relied on to be a jerk...
Just brainstorming ideas - hope things get easier for you.