I think I’ve come to a conclusion about your refutation of S.R.
Essentially as the wheel is turning relative to the train, with a velocity of v at the circumference of the wheel, the entire wheel’s circumference contracts by an equal amount as viewed from the train: the wheel’s radius gets smaller, and is indeed proportional to the amount by which the track (as viewed from the train) gets shorter. The wheel still rotates 1000 times. Paradox resolved, case closed. Sorry.
How is this even possible? Are you saying that the rate at which an observer, motionless with respect to the track, measures the train to be travelling at, will differ from the rate at which an observer on the train will measure the ground to be speeding by? This is nonsense. Think of it like this:
On the roof of the train, there is a sodium light bulb. There is an equivalent bulb hanging over the tracks at the station. Also on the train is an observer with a spectroscope, and there is a second observer with an equivalent spectroscope at the station. As the train approaches the station, the observation of the light from the train’s bulb by the observer at the platform will show that the spectral lines of the sodium bulb have been blue-shifted, proportionally to the velocity of the train. The observer on the train will see an exactly equal blue-shifting of the light from the bulb at the station. This is obvious, and easily experimentally tested. There’s no need to measure lengths to calculate relative velocity; one can do it purely using this method. This avoids any question of whether the observer on the train can measure a different velocity because of the length or time dilation issues - it’s impossible. Plain and simple.