Observation changes conceptions. A full conceptual space-time is pre-observation, not a priori in Kant’s terms because it comes after many observations and experiments. It is a categorical induction: a conceptional scheme that makes observational sense and forms the basis for deduction. That is how science operates.
With a conception of space-time in hand, one may observe and then place the observations into the space-time conception. What happens then is that the space-time may simplify or compress. An observation of velocity makes 6D space-time into 4D: 3D space + 1D time. An observation of lenticity makes 6D space-time into a different 4D: 1D space + 3D time.
The Lorentz transformation is built on either the Galilean transformation, which is 3D space + 1D time, or its complementary form, which is 1D space + 3D time. So even though the Lorentz transformation is properly 3D space + 3D time, it may be compressed into four dimensions in two ways.
Then is there a 6D space-time uncertainty principle, analogous to the one in quantum mechanics? In a sense. The full conceptual scheme is 6D, with 3D space + 3D time. But observation may entail a choice that reduces the dimensionality of space-time. One choice is whether space or time is the independent variable. Or whether space or time is directional. In an observation, they cannot be both at once.