Both my 8 year old son and I have this same set of symptoms, though not as severe. We have both been diagnosed with RAD. Allergies this summer were really triggering RAD symptoms for my son, so I took him to the doctor and he was prescribed Singulaire and Albuterol inhaler. Ironically, this is exactly what I was prescribed when I was first diagnosed, and it worked very well for me.
Since Mike's symptoms are not nearly as severe as your son's, I can't say that I have seen a radical difference since he began treatment last month, though we have had only one instance of increased coughing due to exercise, which was immediately calmed by the inhaler. Thus, I wanted to be sure that you don't rule out the inhaler - I have found that for both me and my son, even one puff on the inhaler before coughing gets into that vicious cycle can stop the symptoms. I used to think the inhaler was only for wheezing and tight chest, but I have since learned to use it at the first sign of the RAD cough, and nip it in the bud.
The other important lesson I have learned is to get the flu shot religously. Every November I used to get the flu, which kept me coughing for at least 8 weeks after recovery. Since I started getting the flu shot, I really haven't had many instances of that lingering, post-illness cough you mentioned. Also, since your son has a history of lung problems, be sure to get him vaccinated for the swine flu as well. I was advised that both my sons need this shot, based just on the fact that they have EVER had a nebulizer treatment (apparently kids with normal lung function should never need a nebulizer treatment).
I also just re-read the other posts and wanted to add that when I was first diagnosed I also took Flovent (I think this is a steroidal inhaler?) and it worked so well that I really didn't need to stay on it (or the singulaire, for that matter). I agree with the others that I would get multiple opinions, and try to get into National Jewish if you are close enough to Denver.
Hope this helps!