I don't know of any who don't have a waiting period but sometimes you see them advertise special joining offers where they wave the waiting period so might be worth keeping an eye out for that.
I have EE
http://www.infantrefluxdisease.com/infa ... sophagitis and one of the thing's I was finding was I was getting a shortness of breath that didn't feel quite the same as asthma and my puffer wasn't relieving it... Do you ever find you have trouble swallowing? What are the diaphram problems you mentioned? My right rib area felt restricted all the time and although the Dr's can't explain the connection since changing my diet once the EE was diagnosed that has resolved.
As 3cherubs said where are you located? I'm guessing maybe overseas (most of us are Aus) I was able to get mine dealt with without using private health (did use a private gastrologist but not allergist) but guess depends where your located as to weather info on how I got into see allergist is of any use to you