My advice is to get another opinion from another vet. Has Garp had an xray? That will tell you if he has fluid in his plueral cavity. Has he had an ultrasound? That will show if he has heart trouble. I can't help but think the vet isn't doing ALL he can if he honestly believes a cat that coughs isn't suffering. If you think there is more to it, go with your gut feeling and get Garp to somewhere else. I didn't go with my gut feeling with Bassett at first, and when I finally did take her to my vet she was in pretty bad shape. Here you have a nad feeling, and your vet isn't responding!! It can't hurt to be safe.. good luck

PS- I'm not trying to bash your vet or be negative.. just if I was in your situation I would get a second opinion. I don't mean to offend