I'm afraid I'm not really a turkey person, but Google says it could be pendulous crop. Can you get a hold of him to examine? Check to see whether it is the crop (it should feel liquid, or like a bag full of whatever he ate last, and massaging it could make him gag).
There are two major problems in chickens.
Impacted crop means there's a blockage, and the turkey can't "swallow" his food from his crop to his stomach. The recommended treatment in chickens is generally coconut oil, (they use coconut because it's solid at room temp, so the animal won't aspirate it. By that logic, shortening, or possibly margarine, should work.) to try and grease the passage so the blockage can be passed. If you lock the turkey up all night and his crop is full in the morning, it could be impacted (or it could just be that his crop has stretched out, and his muscles can't do their job).
A bad smell from his mouth indicates sour crop. It's often treatable with anti-fungal cream, in chickens.
Merck says there's not really a treatment, but they're probably talking on a commercial scale. With chickens, I know they make "crop bras."
According to Poultry DMV, the damage can be permanent after it's swelled too much, so I'd get a makeshift crop bra on him ASAP, check for a smell, give him some oil just in case, and keep him away from food or water overnight to see if it goes down.