You could take him to the vet for an official diagnosis and peace of mind that nothing else is going on with him. If Gordy is wearing a collar I would suggest loosening so it can come over his head easily. He can wear it to hold his tags but not to walk with instead use a harness less trauma to his throat, especially if he pulls.
Our Tootsie has LP, she was around 3yrs when we adopted her. Although her LP was caused by having her vocal cords cut, she has started coughing/gaging more with age. We have started giving her benedryl daily as this helps her breathing and minimized her gaging, plus Pepcid as the benedryl can cause upset tummy. She still romps and plays with her siblings she knows her limits and that she needs to take breaks to catch her breath.
Coleman - CGC blk lab 6/02/97-2/25/08 adopted
Tootsie - choc lab 10/19/99-8/03/13 adopted
Bailey - CGC newf/fc 7/12/00-07/15/14 rescued
Ginger - BT 11/16/05 rescued
Sarah - blk lab 6/22/06 rescued
rescued felines - AJ - 8/00 - 1/11, Merlin - 5/20/05, Tucker - 8/3/10, Penny - 7/7/13