In article ,
writes:

So, we had records from an age of say, 10.7, 11.7, 12.7, and now, 13.7 bill
ion years, where each of those were the observed age of the universe to the
CBR veil, beyond which we cannot observe optically. So we have 3 billion
years worth of observational data forming 4 data points for the distance to
the CBR, and, galaxies that formed from the ancient CBR gas.

Finally, today, we observe the CBR as having come from the last scatterings
of the big bang when the universe became transparent about 13.7E9 years ag
o and we today call that the age of the universe.

We would still observe the evolution of galaxies that formed out of the CBR
gas from epoch 1, 2, 3....with today being epoch 4.

The young galaxies observed would have emitted their light 10.7E9, 11.7E9,
and 12.7E9 years ago.

The problem is, the galaxies at 10.7E9 light years away haven't moved in ra
dial distance over the 3 billion years of observations.

What's wrong?

At least two things. First, you need to understand the difference
between light-travel--time distance (which rarely makes sense as a
distance in cosmology) and proper distance. (There are other types of
distance as well: luminosity distance, angular-size distance,
proper-motion distance.) For proper distance, do you mean the value now
or when the light was emitted? Add to that the fact that the observable
quantity is the redshift, which is related to the scale factor
(independent of the cosmological model). Distance (whichever you
choose) as a function of redshift depends on the cosmological model.
Throw in some non-Euclidean geometry. It's complicated. Read the
literature. There is no point in trying to calculate something, much
less propose something new, if you don't understand the foundations.
You also seem to be confusing three things: the Hubble radius, the CMB,
and the particle horizon. Unless you understand what the Hubble radius
and the particle horizon are and how they evolve with time, it's pretty
much impossible to answer your question.

Again: Take off a few months, read Harrison, UNDERSTAND Harrison, and
come back if you are still confused.