I already awarded the answer, but wanted to add some additional details based on my conversation with the House Rabbit Society (HRS):
HRS, suggested I reduce respiratory stress by mitigating the amount of dust the bunny is exposed to. Specifically, they mentioned finding a hay that is less dusty.
Unfortunately, this isn't likely to help my particular situation as I already have a floor HEPA filter running in the rabbit's cage area (the girlfriend and I are allergic to the hay), and my rabbit actually presented worse problems while the brand of hay that tends to be less dusty (Kaytee) than the more dusty product (Oxbow). I had previously attributed it to Oxbow being more fragrant than the kaytee and thus the smell penetrates the air and reminds them that it's in their feeder so that they eat more. Eating hay helps remove hair balls, allowing for easier breathing.
Nevertheless, I will be on the look out for other brands of hay that might be less dusty than Oxbow but still be as fragrant, and will update this answer if I see a difference. However, agricultural supply stores are not easy to get to from my location, so I might be restricted to mail-order.
HRS also advised I get some video of the problem and/or seek a second opinion. Video is hard to obtain, because he only exhibits the problem when he's relaxed and he's usually more skiddish when he has breathing problems. Nevertheless, more documentation is another good suggestion.
As exotic vet appointments here are running at $110 (and are $160 for the ER if no appointments are available), I was also happy to find out about there Bunny Hop Line which is subscription based on-call (email) vet service that provides you with answers of up to 20 questions for less than half the price of my current vets visit. For those that live far from a vet, this could be a life-saver.
For me, I generally prefer my rabbit see the same vet as often as possible so that they have a good knowledge base around his health and problems. However, I'll likely use this service the next time feel I need urgent, but not emergency care, but can't get an appointment and would otherwise be forced to come in via the ER.