I understand that often you can't find a chicken vet. Can you get to any other vet? Hopefully one would help remove an object if that were the problem.
Sounds like he's trying to cough something out. His crop is empty because it did its job but now he can't eat to refill it. I'm seriously no expert but to me, I'm leaning more and more towards a foreign object.
Did the vet actually see your rooster or just advise on the phone? It could be he tried to swallow something that got stuck. It could be a crop issue. It could be a respiratory infection. It could be a combination of any of these. Check in his beak for foriegn objects. Check his crop in the...