Your time table is concurrent with some experiences we've had ourselves. Fortunately, our veterinarian is also quite like a personal friend (we are a cat rescue/care org.).
There's a question that not only owners need to ask, but these doctors need to keep in their own minds: "Is the animal having more good times than bad? Is there still more pleasure than pain or discomfort in their lives?" At 15 years old and this far diminished, what is this doctor's expectation? A few more weeks? Months? Maybe another year?
There certainly comes a time when the humans in control have to make the decision that enough is enough. It's not worth putting this cat through any more. He's not home. He's not living the life he's come to know in all these years. He's not living a life with more pleasure than pain and no one knows him better than you do. Your instincts are the ones to be trusted.
He's lost most, if not all, of his fatty layers (heat seeking). Just sitting can cause him pain (no cushioning).
I cannot, obviously, make any diagnosis; however, from personal experience it was a cancer. Never did show up in any of the 'tests' and we learned throughout the two year ordeal (we also did everything you've done to keep him alive) that it's not terribly uncommon for this to happen.
We opted for euthanasia, but had the full support and compassion of our vet.
This isn't an easy choice - and I would hope a better dialogue could be established with this doctor.
If you need to talk or anything else, please let me know.
Many have forgotten this truth, but you must not forget it.
You remain responsible, forever, for what you have tamed.