Let me restate my question with a little more specificity.
First, with regard to the PERCEPTION issues, they are fascinating and powerful. Indeed they are so compelling that it is hard to accept the idea that they are only an illusion and many flyers will argue forever that there is a real effect. However, I have convinced my head (not yet my gut) that it is only an illusion - and I am asking about the APPARENT physics/momentum "problem" raised by the example I gave.
I have no problem talking about the perception issues if people want to, but I still would like to see my question answered.
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Yes, I did search this site (and others) before raising this issue but none of the posts comes close to satisfying my specific query. And, I feel no need to apologize for raising this issue, in spite of all the eye-rolling, heavy exhaling that it was certain to create .
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Of course there are different frames of reference one can select, the airplane-air reference and the airplane-earth reference, to name two. My question is asked from the airplane-earth reference frame, which is perfectly valid. After all, gravity is a major part of this situation and it is relative to the earth, not the air mass.
Newton's laws should be totally resolvable from ANY of the reference frames anyway. Furthermore, since we are not dealing with relativistic masses and velocities, we don't need Einstein to resolve this matter. Newton will do just fine. So... inertia IS an issue, pretty much an ABSOLUTE issue in fact.
I like the dog-on-the-train analogy. Even with it, one can resolve the inertia/momentum issue easily. Any change of speed by the dog has to be translated to the train and thus to the earth, so there is no momentum "problem". For example, the dog (running forward) decides to stop. His momentum is transferred to the train and it speeds up a tiny bit. He starts running back and the train slows down. The momentum of the train relative to the earth is affected and, if the engineer hits the brakes, this force is transmitted to the track and then to the earth. Ultimately the earth "feels" the dog's inertial effect.
Once again, Newton's laws should be totally resolvable from ANY of the reference frames anyway. Even the airplane-airmass-earth-traintrack-train-dog reference frame (the "airplane-dog" frame for short) should be completely resolvable as to ANY momentum changes.
I guess the air mass is the train and the dog the airplane. However the plane is not coming to a stop but going through a curved path while maintaining airspeed. This introduces angular momentum into the picture and it gets even more intellectually muddy for me, which is why I am looking for help.

Regards,
Allan