My problem isn't with my airways, but with the other side of the equation, the blood supply to the lungs, but the effects are similar. I get out of breath much quicker than I should do, especially for the first hour of a ride.
I have found that things are gradually improving though. It is 4 years since I was hospitalised with a massive Pulmonary Embolism and 3 years since the second one. It has taken me about 10,000 miles of hard, hilly cycling to get back to where I am now.
I push myself when feeling okay, and back off when I start to struggle. It probably confuses people that I ride with, because one minute I am shooting off the front, the next I am way behind! It suits me better than just plodding along at a constant easy pace.
My doctors were happy for me to exercise as hard as I wanted to, and just said "listen to your body", so that is what I do.
PS That is not strictly answering the OP's question, but I think it is good to read how people try to overcome their health problems. When I got ill I read as many 'good news' posts as I could find. My doctors said that many patients just rely on drugs to try to fix their problems for them when they could have much better outcomes by also eating better food and exercising regularly.
Keep on riding, and good luck with the COPD!