In article , Eric Flesch
writes:

One of the models that I'm juggling treats time dilation as the
square root of the redshift,

Is there any physical motivation for this?

Yes, one model of "geometry of look-back" is that we see the past as
smaller and slower than the present, because of the drift of a (new)
cosmological factor.

Unless there is some physical motivation for this OTHER THAN explaining
the observations, this seems a rather ad-hoc solution.

This maps into seeing the nightsky as an
open-manifold universe with a redshift. So this proposes to swap this
one new cosmological factor for all of yours (dark energy, etc, you
know what they all are).

All? The only thing remotely strange is dark energy, better known as
the cosmological constant, and mathematically that has been around for
100 years. Interesting that when observations indicated a slightly more
complicated universe, it turned out that 1920s cosmology already had a
solution. Dark matter? If that is strange, then that means that the
default assumption is that all matter glows, which seems strange to say
the least. Non-baryonic matter, meaning most of the universe is made
out of something we are not? Is that strange? Most of the matter we
know about is in stars, but we ourselves are not stars, and no-one finds
that strange.

But I have to well-fit this to all observations, which is daunting for
me, since so much observational data is published only as
post-FRW-processed data, which is hard for me to decode backwards.

Not only that, but often interpreted in the light of a certain FRW
model.

I
may indeed have to do as you and Steve Willner kindly suggest, which
is to request the original data from the authors.

I don't think that will be a problem. Many data are available today
even without asking---usually not directly in publications, but in
online resources mentioned there.

Similarly, I wish to
economize on all the magic tropes of modern cosmology,

Again, modern cosmology is surprisingly boring. Recently, the 9-year
WMAP papers appeared on arXiv. A huge amount of data, and no
indications that we need to revise our cosmological model. In
particular, the large-scale model is, again, 1920s cosmology.

and remind all
that things flying apart at high speed is no way to model a universe.

Unless you have a really, really, really different theory of gravity,
you have to explain the stability of the universe if it is not flying
apart.