"Our question, however, states that the conveyor must match the plane’s wheel’s speed.
In this case if the plane moves forward, its wheel has gone further, and therefore faster than the conveyor. The only thing that the conveyor can do about this is to speed up like mad!"
No, no, no. The wheel must go at exactly the same speed as the conveyor. it MUST. Lets say the wheel moves at 1ft/sec, (I am assuming you are measuring the wheel speed along the circumference as it rotates CCW right?). then the conveyor is moving at 1ft/sec. I The plane speed, assuming no drag or mechanical failure is , 1ft/sec relative to a stationary object. There is no magic here, that i can see. I am open to counter argument though. But the WS=CS must hold true! The question binds that. The argument that it is impossible for the conveyor and the wheel to move at the same speed at the same time may be true, but that is not what we are given.
I think what would be happening is the wheel would be skidding along the conveyor. But, let me tink about it .