The direction of increasing entropy being fixed puts no restriction on how that is represented.
Even without absolute time, I don't see how this is true (emphasis added; italics in original):
"In the big bang scenario, the beginning of the Universe is characterized by a past time-like curvature singularity (where time itself began). Penrose used this fact to postulate his Weyl tensor hypothesis on all past singularities, since this would allow only
one of them: a uniform big bang.
In the absence of an absolute direction of time, the past would then be distinguished from the future precisely and solely by this asymmetric boundary condition and its consequences" p. 139 of
The Physical Basis for the Direction of Time (5th ed.); Springer, 2007.
"the theory of general relativity predicts a warping of space and time which is directly proportional to the energy density distributed in the matter sources. By applying this theory to our expanding Universe one then obtains a cosmological model in which the curvature of the Universe itself evolves with time, following the corresponding evolution of the energy density and temperature." from The Universe
Before the Big Bang: Cosmology and String Theory (from the series
Astronomer's Universe): Springer, 2008.
Even in cosmological models (e.g., those which use Desitter geometries) where the thermodynamic basis of time breaks down, either this is replaced or it is deemed a problem of the model (such as an issue with the cosmological constant) because this does not cohere with observations. Time doesn't run backward. "This result would be in a huge disagreement with observations. We do not observe a reversal of the arrow of time in our DeSitter universe, in time scales of the order of the age of our universe." p. 57 of Mersini-Houghton's "The arrow of time in a universe with a positive cosmological constant" in the edited volume
Cosmic Update: Dark Puzzles. Arrow of Time. Future History from the series
Multiversal Journeys.
but why should that make a difference?
Because virtually all models can be run backwards and forwards with respect to time, but unless this is meaningul for physical theory, the math doesn't matter.
(Also, CPT symmetry is universal, and the signs of charges don't matter for the argument.)
As Bigi & Sanda put it in the opening of their book
CP Violation (
Cambridge Monographs on Particle Physics, Nuclear Physics, and Cosmology, vol. 28), the disparity between how we experience time and how it is described in physics could (we hoped), be "understood" if "microscopic T invariance" existed in such a way that the same invariance is "so unlikely to occur for a macroscopic system." However:
"It came as a great shock that microscopic T invariance is violated in nature, that ‘
nature makes a difference between past and future’ even on the most fundamental level."
After all, God
is supposed to be outside the universe and unbound by time.
You'll have to take that up with God, unless of course God starts contributing to physics literature.