I tried really hard to eliminate, as much as possible, litter-related dust. I switched to a paper-based litter to accomplish this, and there is virtually no dust. I guess a way to see how much dust kitty might be stirring up is to just swish your hand around in a litter pan a bit and see how much puffs up. The brand I first had for my girls was awful, even though it said 98% dust-free. The poor things had litter dust caked to their noses (does your kitty have any of this inside her nostrils?). I switched in the first week I had them home.
This has improved Goblin's coughing (she has had sporadic outbursts, too). Her other issue is indeed - hair. I now give her laxatone regularly and she now very rarely has these episodes.
If your cat's episodes seem centered around the litterbox, I'd work from that angle. If they happen sporadically at other times, perhaps try the laxatone.
I guess my only other thought is - does kitty have a weight issue?
Bottom line - if you're not happy with your vet and you really think there's something wrong, there's nothing wrong with seeking further dialogue with your existing vet or asking for a second opinion. Tell them your concerns of the cough continuing, etc. Personally, it might be worth a shot trying a couple of environmental changes first though, to see if kitty is senstive to dust or allergens, or having hair issues.
I hope kitty improves!