I keep coming back to entropy because the asymmetry in entropy is one of the things that needs explaining
Again, why bother with entropy as such? Just say "the initial conditions need explaining" and be done.
Given any criterion for distinguishing macrostates, you can (in principle) compute entropy relative to that criterion.
I do not understand how these two paragraphs are a response to what I said. Can you elucidate?
So far as I am aware, there is no reason to think that weak parity violation is responsible for the familiar macro-scale time asymmetries everyone notices.
Electroweak unification. That aside, the original problem was "there is no asymmetry in the laws of physics that can cause [macrolevel asymmetry]; Newton's and Maxwell's (and Einstein's) laws are the same in either time direction". And then we realised that yes, there is an asymmetry in the laws of physics. Well then, that solves the problem; what more do you want, unfried egg in your barley-that-used-to-be-beer?
why bother with entropy as such?
Because it's one of the more obvious descriptive statistics to look at and it shows the difference nice and clearly. If we just say "the initial conditions need explaining" (or: the differences between initial and final) then the obvious question is what about the initial conditions, and part of the answer to that is going to be the entropy. (Or maybe some other thing that's essentially equivalent.)
Also, because it's a statistic that not only is different between the distant past and the distant future, but also...