But if we subtract this (presumably minor) effect from the observed redshift of distant galaxies, we're necessarily left with lower expansion speeds. In turn this means there's less need for gravity to hold them together in the various structures we observe from the galactic level up. This has the implication (I presume) of affecting inferred requirements of dark matter and dark energy.

However, what observations (besides assumptions about the source of background microwave radiation) are consistent with the pejoratively-named BigBang theory? We don't even know how big the universe is. It mat be far larger than the observable universe. And all the pocket universes are technically part of the same multiverse -- what makes us think there was for sure a big bang?

All that the "Big Bang" refer to is 1) the fact that the (visible) universe was once much hotter and denser than it is now and 2) if we extrapolate back in time, using the theories that we have, there was a point where the density was infinite.

Of course, we know that our theoretical model break down before that (since we don't have an experimetally verified theory of gravity compatible with quantum mechanics). Physicist that work in the field (and I used to be one of them) are well aware that we cannot extrapolate past the regions of validity of our theories and no one claim that there was indeed a singular point ("Big Bang") as mentioned in descriptions aimed at a non-expert audience.

I am pretty sure it's not true that "no one" claims there was not a singularity at the beginning.

http://www.hawking.org.uk/the-beginning-of-time.html

I even saw that recently Stephen Hawking started theorizing that the "Big Bang" was like a black hole. And other physicists weigh in:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/...

Look at this wikipedia article. Someone must be writing it?

https://en.m.wikipedia.org/wiki/Initial_singularity

In fact there are some contradictions between Quantum Mechanics and an actual big bang:

https://m.phys.org/news/2015-02-big-quantum-equation-univers...