Dear Jonathan Kerr,
I enjoyed your essay immensely, and not just because you focused on the fundamental nature of time.
You ask exactly what I mean when I say SR implies two time dimensions. I base this on Rindler's definition of inertial frame as one in which spatial relations (as determined by rigid scales at rest in the frame) are Euclidian and in which there exists a universal time [such that Newton's laws of inertia hold] and on Einstein's formulation of his two principles of relativity in terms of (at least) two inertial frames.
One might say the "universal time" is the same in both inertial frames, but Einstein goes on to derive the Lorentz transformation in terms of t' =/= t, so that the times clearly are not the same universal time. That they can share one time t' = t = 0 in common does not make them the same time. If they had no point in common they would be impossible to relate to each other, effectively separate elements of a multiverse. The Lorentz transformation of 4D entities mixes time and space based on the idea that the time axis can be rotated from t' into t. If there's only one universal time then t' = t and it does not mix time and space.
As I develop in the essay, time does not 'dilate'; it 'flows equably through all space'. Local "clocks" measure energy, which is conjugate to time, and each 'tick' is a measure of a local time interval that is characterized by the energy of the clock mechanism. Motion-based energy differences of clocks do not represent variations in the time dimension, which is simultaneous across all space.
Daryl Jansen, back in the day, argued strongly that the 4D block time is nonsense and that any discussion of it immediately introduces a fifth dimension where things change. Nothing changes in block time. It exists only because of the Minkowskian idea of 4D rotations in 'space-time'. If time does not mix with space (it doesn't) then the 4D block time is a mathematical artifact, having no physical reality.
I agree with you that conceptual physics is the best way forward, but many react to new concepts as if they were the plague.
Thanks again for reading and commenting on my essay.
Edwin Eugene Klingman