You could try a Flexi, but I think Judi meant letting him drag a piece of long line. Something like a 25' foot yellow nylon cord ? Any hardwear store sells it.
If you took him to an area away from traffic and just kinda walk behind him without looking at him and give him the command to "poop". Then treat and praise as if he were a puppy.
I also think if you use the papertowel trick...make a few spots in your yard...he may get the hint and go in the same area.
When I first got my rescue, she was the same...would not poop on a leash.
The whole family took turns walking and walking her for miles...and no poop. I have a dog run behind our house and put her in there thinking that she needed her "space". Sure enough she went within a few minutes.
What does help is timing. Feed the dog, and then go for a long walk on a Flexi or longer leash....feed some treats while you are walking. If the dog slows down and starts sniffing...just stand still and look up and away.
If the dog does go in your yard...leave the poop there....it may encourage him to use the same spot again.
I am having problems right now because our snow is so deep and we cannot walk through the fields for our poops.
I got hubby to blow with the snow blower, pooping paths for the dogs. Our pup is finding it weird to be pooping in a fairly small area. He now finally understands that he can poop close to the house, after being taught all summer to poop in the long grass away from the house.
The do learn.
Gina