Hi there Rain.
I dont think Neil is angry, or trying to get revenge. Cats dont do that, in spite of what we sometimes think. He's trying to communicate because something in his world isn't right any more, and he needs you to lend a hand.
I know you've indicated your vet has given Neil a clean bill of health, but to me, it seems he's exhibiting signs of hyperthyroidism, which is quite a common condition in older cats.
Yowling is a well known side effect, as is eating more. One of the effects of Hyper T is that cats never feel full, even when they're eating regularly.
Untreated Hyper T can also lead to kidney problems, and if he's feeling uncomfortable that can cause inappropriate toiletting (although bless him, at least he's using areas which can be relatively easily cleaned!)
Does he have a litter box in the house? If not, I would suggest it would be appropriate to provide one, or perhaps two (one upstairs and one downstairs) . You might have to experiment with different types of litter until you find one that he likes.
Cats which are Hyper T often display more restlessness and "neediness" than they have previously done. They want reassurance, and that may be why he's objecting to closed doors.
We had Paddy until he was 20, and he first began to exhibit signs of Hyper T shortly after he had a stroke, when he was 15.
Hyperthyroidism can be treated with medication (there are other options but they arent always viable - much depends on the individual cat). I think I would suggest taking him back to the vet and discussing the symptoms that you're noticing, and they can test for hyperthyroidism.
Do you have any piccies of Neil? I bet he's gorgeous!
