Thrust from the plane will make the wheels turn as the friction in the wheel bearing is less the the friction between the tyre and the conveyor, just as it makes the wheels turn on a proper runway - can we agree that?
nope, can't agree at all Oil on oil = low friction, rubber on rubber = high friction .. You appear to have completely reversed your own logic i.e. if there is no or low friction then you will get slip, let me put it this way, there is no force to turn the wheels, just because the aircraft is moving forward it does nothing whatsoever to turn the wheels other than the wheels are rolling on the belt! ... now if the belt is running in the opposite direction what it is actually doing is simply turning the wheels at a constant.. the only possible force (of any significance) if the wheels are turning is from the belt, the speed of the wheels in any direction has absolutely no effect on the planes ability to push or pull itself through the air
The control mechanism you describe is impossible as it cannot sense the movement and react to counter it instantly, c intervenes, there has to be some lag. Lets say it is one nanosecond, that is about as close to instant as you can hope for.
It doesn't have to react instantly as the wheels and belt are actually independent of each other i.e. there is no mechanical linkage other than grip / friction, also the conveyor could not react instantly.. anyway it is totally irrelevant and moot as the wheels do not interfere with the planes ability to move forward or not!
Lets say the cicumference of the tyre is 1m. In the first second after the engine is turned on the tyre rotates 360 degrees. In that same second (with one nanosecond lag), the hypothetical control mechanism on the conveyor moves the surface one metre in the opposite direction. Where is the plane now, relative to where it started? If it is not in the same place (to within 2x10^-9 metres), please explain where it is, with reference to the conditions you laid down at the start, because in that case I will have completely misunderstood your description of the experiment.
I think here is where you have confused yourself The plane is only moving relative to the air around it and has nothing whatsoever to do with the ground (or belt) other than from a visual viewpoint
Actually, the newly functional LHC will create a mini black hole that will swallow up the plane and in an amazing co-incidence I will find the missing massive scalar boson predicted by Peter Higgs down the back of my sofa, thereby proving the Standard Model. Physics will be solved and planes will be obsolete because we will have teleporters.