You can’t imagine how refreshing it is for me to run across a real thinker.
It just so happens that I am writing a paper on that very subject (except concerning photon and electron spins). And you are right in that the dilation effect would calculate out to be far more complicated than a simple oval. But you don’t really have to calculate out the entire exact values. Every point on the wheel will be more contracted than it was as a circle. So even though it won’t be a symmetric oval, it will certainly be more narrow. There is no point on the wheel that has any impetus to be greater in diameter.
The center of the wheel would obviously be tracking the speed of the train. The top of the wheel would be twice the speed of the train, thus the top would contract even more. The end result is somewhat of an egg shape, still never as round at any point as the circle or the height in diameter.
And yes, time dilation in the direction of motion must bring the spin to a stop as any spinning object reaches light speed. Interestingly, the transverse spin does not change. And even more interestingly, what that means is that every atom in an object moving near the speed of light, will form a magnetic dipole and become a magnet. Even a block of wood, would develop a magnetic field and crush itself. The properties of materials completely alter at extreme speeds.
So the short answer is that the wheel must still seem to have a shorter circumference when it is traveling faster.
And I might add that from the train’s perspective, the wheel becomes a bit egg shaped too. The horizontal diameter remains the same, but the lower half gets larger as the upper half gets smaller. This forms a squashed egg shape. But the upper and lower halves, in effect, cancel each other’s circumference effect.
But great observation.