To me, on the surface at least, this one seems more straightforward than most urination issues. It really doesn't seem like a marking issue, so I think we rule out stress or territorial behavior. I think he's simply rejecting that litterbox. He's in effect saying "I'm a good kitty, and I know where I should go, I want to go there but I just CAN'T because...". It's the "because" that we have to figure out. It's clearly not the location. I would say that he either dislikes that litterbox, of he's having a medical issue which would cause him to associate the litterbox with discomfort.
So questions:
1. How old is the box? Is it possible that it is just "smelly"?
2. How large is it?
3. Is it open or closed design?
4. When he rejects it, is there poo or pee in it?
5. How often is the litter changed?
6. Has the type of litter changed?
7. When he goes outside the box does he first go inside the box and then walk out and decide to go outside it? Or does he just walk right up to outside the box and go?
8. Is there any blood in his stool?
9. Does it look like he might be struggling to go on occasion?
10. What is his poo like when he goes outside the box?
The easiest and cheapest thing to do would be to go out and buy a new box (hopefully larger and open design) and see what effect that has.
P.S. The "reasonable location" thing is really his call
Your only clue as to the reasonableness of a litter box's location is simply how frequently it gets used