Check the hinges again. Pretend that you are doing it for a customer which you do not like. The doors are heavy. Bend your knees and really pick up on it at the rear end of the door and look for movement.
Worn out hinges eventually feel "tight" from galling and rust. They will still sag, so you need to double check before you try something else and end up chasing your tail.
Been there, done that. It turns out that I do not have a tail..
