Do you remember where I said you need to think of quality of life over quantity? You are way past that point now. He is emaciated, he is in constant pain, he cannot eat enough to sustain himself. He can't even sit comfortably. Even one of the things you listed for his diagnoses are hard to treat, he's got several and the treatment is not working.
Tell this vet to STOP treating your chin like some kind of experiment so he can figure out what to do next time. That's what it sounds like he's doing. A vet cannot refuse to put down an animal. Remind him of the oath he took when he became a vet. He swore to relieve animals of suffering. Your boy is suffering.
Hard reality - eventually, your boy will dwindle away to nothing. He will be in terrible pain. His organs will shut down one by one. The stress on his body will cause more and more stress on his heart until eventually, everything slows down to the point where he can't function anymore, where he can't fight anymore. Then you will find him laying on his side in his cage, gasping for his last breath, possibly seizing, and you'll think to yourself "I wish I would have put him to sleep." Only by that time, he will have suffered more than any beloved pet should.