I think your confusion comes from the shape of the treadmill...
There is a very big difference between the two cases and key in understanding what will happen in my diagram and why vehicle will not be able to move from left to right if you use a treadmill.
The one that is confused here is you. None of us actually have any doubt about the fact that the Blackbird works as advertised, even though some of us (me, for example) had the same initial reaction that once the vehicle was at wind speed, there doesn't appear to be a source of power. A little thinking, read my reply#20 or any number of others, and we all now know how it works more or less. And none of us have any doubt about the outcome of your treadmill example. Your insistence that it 'must' work is a bit like insisting that the moon is made of cheese--with no proof or theory--and responding to all arguments with "just go take a bite--you'll see!"
All of my questions of you have been directed at finding out where your misconceptions lie so that I might reason you out of them. Unfortunately I think that the answer is that you have a very basic lack of understanding about knowledge itself when it comes to the physical sciences--the concept of manifestation, to start. Physical phenomena involve interactions that manifest themselves (which simply means they appear) in a sensible (which means detectable, capable of being sensed) way. We use different terms and concepts to describe and define these interactions--guage bosons for quantum physics, electric and magnetic fields for optical and electronic systems, etc.
For basic mechanical systems, the interactions are defined and described by simple
force. Other concepts arise, such as LaGrangians and Hamiltonians, conservation of momentum, conservation of energy, etc which can be applied
where appropriate to solve problems where force concepts become difficult to understand directly--but they all are derived from the original simple laws of force and motion. Simple mechanical systems (and these are all simple mechanical systems) can only sense force. If something changes the state of an object, it has to involve a force. The force that something may apply to another system or object is dependent on its sensible characteristics--sensible in this case meaning those characteristics that will make a difference in its interaction with the other, or IOW can be sensed by it.
In the case of your diagram, the only relevant characteristics of the paper are the physical characteristics of the paper itself and the rate at which it is moving. If you think there is some other sensible characteristic--one that an observer could see by only looking at the moving surface inside the frame as I proposed--please tell us what that might be. Otherwise you have the same paper, moving at the same rate--and there is no reason that the car would behave differently from one to another nor any way that an observer would be able to notice the difference. There is no sensible force or phenomenon that would cause the interaction between the car and the paper to be different in either case and there's no magical subspace phenomenon that will intercede because you think another law has been violated elsewhere.
Stop imagining that your brain can magically intuit the intricacies of physics. It is totally counterproductive and will greatly impede the learning process. Intuition is a layer on top of learning that can allow you to leap ahead of actual calculations a bit, but if it only lies upon minimal knowledge, or worse, misconceptions, than it will lead you pretty far astray. I have no idea how you convinced yourself into this mess of misunderstanding, but your refusal to reexamine your so-called conclusions or your reasoning process is not an indicia of intelligence, but rather of exceptional hard-headedness. And coming from me, well that's like Chris Farley calling you fat.
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