Think of the conveyor belt runway thing like this to show that the speed of the conveyor (and hence wheel speed) has absolutely no effect on the take-off speed of the aircraft:
If the take-off speed of your plane is 180mph, then make the runway move at a steady 180mph FORWARDS, but hang on to the plane so that it's stationary. This will make the wheels of the plane move in reverse - right?
Ok, now wind up the engines so they start to develop thrust. (Then stop hanging on to it so that it can move) Obviously the air around the plane is still stationary. Will the engines have to move the aircraft forwards at 2x180mph for it to take off? (As that's when the wheels will be doing 180mph relative to the conveyor) Of course not - the aircraft will still take off at 180mph relative to the air around it. In fact, in this case, the aircraft will take off when the wheels have just stopped moving.
So, you can see that the wheel speed has absolutely no effect on when the aircraft will take off as it can still take off even if the wheels are not moving at all.