You usually impress me with your efforts and knowledge but I have to disagree with you here. That said, it may be that I do not have enough information from your post about what happened to you.

If I recall, you had a problematic Long Thoracic Nerve which was impinged/entrapped by a variety of things. IMHO one of which could have been your hyperinflated lungs (certainly enlarged lungs or ribcage would impinge on nerves etc).

When you say "soft ribcage" it sounds merely like the medication helped to reduce the hyperinflation. Which in turn reduced the space and possibly compression of the LTN. This, if true, would possibly be why you are being helped.

could it have been accomplished without medication? Sounds like you had some kind of condition that required the medication to help you breathe more "normally" so that you wouldn't have this hyperinflation. I know you had tried other methods to deal with your TOS.

The disagreement lies in the analysis. In your case, yes, posture might not have helped. Then again it may have. In many situations POSTURE is key. Yours may be one of the more minority versions where it isn't. So I have a hard time when you advocate "forget posture"

The ribcage is one of many structures that is a culprit in many TOSers symptoms. I have a new "pain" or sx that I've noticed (actually it's not really new, it just recently came to my forefront in attention) but it relates to my ribcage...go figure. So now I'm being given ways to lower my ribcage...again to increase the space and relieve any compression. In my case...it appears, if I understand this correctly, that my rib cage is drawn up by the scalene (attached to the first rib)...if I can keep the ribcage down...I can reduce or eliminate the compression. It's a tricky thing to isolate these muscles but I understand the goal and why. To me this still falls within the realm of posture/position/alignment that I still feel is very key with the majority of TOSers.

I love ya guy...hang in there. More power to you finding something that is helping you.