Well, gravity is not typically involved in entropy calculations, though you do see it involved in black hole calculations mostly to ensure that entropy cannot decrease simply by going over an event horizon.
Well, unless you want to have some fun - I'm sure it's been torn apart in the meantime, but you can have a gander at Dr. Verlinde's expression of gravity as an emergent property of entropy
seem to beg for a beginning of some sort, but it seems hard to reconcile low-entropy conditions with Big Bang conditions. I haven't read deeply enough into the literature to see how they modify the description of entropy - but it seems like it must be modified, because without asymmetry in the expansion, none of that initial energy would be usable to do work, and that's the very essence of a highly entropic state. I can see expansion plus asymmetry pushing entropy lower, but to the purist for whom entropy can never reverse itself, I am sure that the "potential for expansion plus asymmetry" would have to be jammed into a more encompassing description of entropy. I wonder if anyone's managed it properly.
Intrinsic redshift certainly would gum up the works. It certainly seems as though the center of galaxies would come into play one way or the other, whether the variable mass hypothesis (I wonder if Narlikar has done entropy calculations on that) or otherwise.
Just a quick aside on particle creation - from various things I've read, it seems that particle pairs form most readily in the presence of energy and charge in particular more so than just mass. The E-M fields in light are sometimes sufficient enough that aiming energetic light beams directly at one another is enough to generate particles, even though otherwise, gamma rays can travel from far-away bursts.
Maybe it's like this. Vacuum energy and the quantum foam conjur up some particle pairs, and from prior reading I recall that particle pairs are more likely to form near mass. Perhaps this produces a runaway process tending to form these massive objects (black holes?) that ultimately become the center of galaxies. If this is the case, it might not even matter if the expansion of spacetime is real, as matter keeps getting created in a bunch of mini-bangs, so to speak.
That actually sounds a lot like Hoyle, Burbridge and Narlikar's QSSC. It's quite bizarre - it involves a "C-field" very reminiscent of the mainstream "inflaton field" that accumulate in gravity centers but with negative pressure that "mini-bang" or radiate away when it overcomes gravity - but it has the exact features to which you refer :)
Happy Birthday, by the way!