I agree re not communicating... I'll take one more shot at communication, last try

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Re. 1: I did not interpret that you were talking about breath moving through the sax; I simply stated that no air is actually traveling anywhere in the propogation of sound, "save for the amount being breathed into the horn". That wasn't an interpretation of anything you had said.
Re. 2: "Bounce" and "Reflect" are equivalent terms regarding sound waves. I think we can agree that a metallic wall can reflect a sound wave, as a starting point.
Re. 3: I've never talked about standing waves reflecting. Even 'though they only exist because of a reflection. I've talked about higher frequency waves, where the wavelength is substantially shorter, shorter perhaps than even the diameter of the horn, there is ample opportunity for those frequencies to be reflected around. It is in fact very useful to study water to understand wave behavior. We spent a semester in college physics with wave tanks. Much of wave behavior is not only shared between water and air, but even extend to light when being considered as waves. Reflections, propagation, interference, for instance, are substantially consistent between these.
Re. 4: Yes of course. My only point, which was not in conflict with anything you had said, was that the description in the Morgan paper was perhaps confusingly worded in talking about "air vibrating in and out" of the tonehole. And only to say that it infers (or at least to me) that air is moving in and out of the tonehole. If you want to measure tiny distances and call that "in and out", then fine. The distance, at high frequencies, that air molecules are moving back and forth is so small it would be hard to say at what point a molecule might be in or out. The sound wave is what travels through the tonehole to one's ear.
Also Re. 4: I did not remotely say that the minute movement of air molecules is of no consequence. It is the entirety of what sound is. To call my concepts of acoustics "dodgy at best" is probably too far removed from the topic to justify more than a mention if at all.
Regarding your suggested experiment, I don't need to do it to know and understand that it would be as you describe. Lower frequencies will have much higher amplitudes of movement, just as a woofer has greater excursion than a tweeter. I was discussing high frequencies with short wavelengths (think tweeter) which have much lower amplitude. And that discussion was specifically in relation to the use of the word "reflection" off of resonators. Which I think is a completely acceptable use of the term especially in that context. Just to bring the conversation back to what started it. Reflections of high frequencies are of great consequence and the design of high frequency drivers for audio goes deeply into controlling reflections to avoid interference and phase issues. In the same way, reflections of high frequencies in a horn could potentially have an effect on tone characteristics. Noyek or "waffled" resonators, in my experience, have a definite effect on upper harmonics. I don't know to what, other than reflections, one would attribute that.