Thanks for all your kindness. For the first time in a couple of days, he came into the kitchen with me, and watched like a hawk as I opened the fridge. I took the opportunity to take out a few tiny pieces of chicken, and heated them in the microwave for a couple of seconds, just to warm them to body heat. When I put them down for him, he just put his head down, poked the scraps, and then wandered off again. On the plus side, walking to the kitchen was more than he's done for a while, but he was painfully unsteady, and obviously without eating anything, and drinking only tiny amounts of milk or water, there's no way that he can keep his strength up, let alone start to recover. From that aspect alone he might be better off at the vet's, where they can nourish him through an IV drip, and can also get him back on oxygen if his breathing deteriorates, but he doesn't seem distressed, so I might just be looking for an easy way out, just to save me again.
I could try mixing blood in with the tablets, as he seems to be getting a taste for it, but I'm concerned that he might become that most dread of creatures, a Vamcat, and then decide just to sup straight from the source.