Or maybe it's simpler, and movements faster than light are possible, but not detectable by humans due to the lack of a corresponding sensory organ?
Example: a blind person "observes" the movement of a supersonic aircraft. The aircraft has long since flown from point A to point B, but for the blind person, it still seems to be in point C (between A and B), because the sound lags behind.
1) the effect of relativistic time dilation really does exist
2) in special relativity, it is explained precisely through the fundamental limit of the maximum speed and the equal speed of light.
If the speed of light is not a fundamental maximum through which all transitions to other frames of reference are calculated... then time dilation needs to be explained differently.