Time Reversed Cosmology

One of my favorite authors is Greg Egan, and that's in great part because of how in many stories he starts with known physics, adds a twist, and follows it to its logical conclusion within the story's setting.

A particular idea he's used a few times is the idea that portions of the universe could potentially contain "time-reversed" regions. From our point of view, for instance, a time-reversed star absorbs photons, and if we could observe biological phenomena they would likewise go in reverse. (See e.g., the short story The Hundred Light-Year Diary)

From our point of view, the universe began billions of years ago with the big bang, and as far as I know all present observations are compatible with zero or negative curvature. This apparently gives an infinite amount of time to come in the future, though only a finite portion of that future can support baryonic life like ours.

So what does cosmology look like for the time-reversed universe, and what are their "big problems"? I don't have enough background in basic physics and cosmology to give a really good answer to this question, but here are some things that occur to me:

How to reconcile the apparent flatness of the universe with the observed cosmic blue-shift
If the universe has an infinite past, and the baryonic era has been going on for at least 10³⁶ years, why are there no other observable civlizations?
Were natural laws different in the distant past? Why and when did baryogenesis occur, given that in the present day the creation rate of protons is so small as to be unmeasurable? Ultra-low energy / density physics will presumably be an area of great interest in understanding the origins of the universe.
At the same time, high energy physics will be of interest in understanding the fate of the universe. Scientists learn that in the high-energy future, the laws of physics themselves break down ("unify" in our terminology).
Some models will predict a "deflation" process that begins when a certain mass/energy density is reached, rapidly collapsing the observable universe and obviously destroying all intelligent life in the process. Unfortunately, the models will be unable to predict the specific energy density.
I'm not sure what the time-reversed CMB looks like. A white-hot wall that indicates "deflation" is already going on in the distant parts of the universe, an approaching wavefront that clearly dooms all intelligent species?
What, if anything, happens after the great singularity at the end of time?