@alureon, sorry to read what you're going through. For me, intense exercise made my condition worse. I remember when my breathing was fine for a while and then I increased my running and ran faster and harder, my air hunger came back suddenly and with a vengeance. I had to stop exercise for a while and start very slow again and work my way back up. I now go for a run maybe once or twice a week, and mostly do light to moderate weightlifting about 5 times per week. My runs are really mostly walks with short bouts of jogging in between. I just listen to my body and if I feel the SOB coming on stronger I walk the rest of the way home or stop if I'm on the treadmill. But weightlifting seems to help me the most because I can control my breathing and work out as intensely or light as my breathing will allow. You might consider incorporating light weightlifting using only nasal breathing rather than hard running with maximum breathing. At least for me, I've learned that it doesn't seem to have anything to do with lung capacity since my lung capacity tests have all come back normal. Intense exercise doesn't help to expand my lungs, even if it did, the SOB would still be there.
Regarding the SOB vs. air hunger, yes I think we all have the air hunger feeling where we can't satisfy a feeling of a need for air. I guess for me shortness of breath means air hunger, where as "out of breath" equates to a normal feeling of a lack of air while exercising, but in that case it's not uncomfortable because heavy breathing still satisfies the need for air. Semantics, I know, but in my mind shortness of breath means just that, that you're "short" of breath since the "need" doesn't go away even when you take a deep breath.
Anyway, I hope you improve soon. Keep us updated. I don't think it will hurt to try something different; taming the exercise and doing shorter and lighter sessions while incorporating weight lifting and using light, slow breathing. That's what at least maintains my breathing at a manageable level.