I also would think that rotational movement is not movement through spacetime, even if it changes the "1st person" frame of directionality (forward is now right, then behind you, then left, etc.), it doesn't change the reference of ones position in spacetime. So, even if you were rotating at a constant rate in the vacume of space, not accelerating, your frame of reference is the same as that of a rotating planet or star.

The night sky "spins" at well above the speed of light for the furthest stars, but that's never contradicted relativity because that's based on position, not rotation, over time.