Maybe you can dig up a reference, because you're on the verge of telling the conventional cosmology in a time-reversed way.
Under time reversal eventually the very first stars disintegrate into mostly atomic hydrogen, which compresses and heats adiabatically. Eventually it becomes hot enough that the hydrogen ionizes. Ignoring processes which alter photon number, the hot nuclei and electrons form a dense fog.
As with a fog here on earth, where incoming light can get bounced in a random direction off a fog droplet ("Mie scattering"), photons scattering off these hot charged particles are scattered in a random direction ("Compton scattering" at high energies, "Thomson scattering" at low energies). When we densify the fog, the free-streaming length of light decreases, increasing the fog's opacity.
Under the normal direction of time, therefore, the CMB is when de-ionization enormously shrinks the analogue of the fog droplet size ("Thomson cross-section"), and expansion increases the distance between the fog droplet analogues. The free-streaming length can become effectively infinite, like clear night air after a fog dissipates. The spectrum of the light at that point encodes the effective temperature of the scattering medium. In an expanding universe, that spectrum will lose energy (i.e., redshift).
The electrically neutral mostly-hydrogen then takes three principal forms: collapsing clouds of gas, which eventually form the first low-metallicity stars; cold dusts of neutral atoms at various sparser densities; and a warm-to-hot sparse intergalactic medium. The latter two is where we should find the so-called "missing baryons", the large fraction of atoms not found in stars and galaxies.
Backlighting by active galactic nuclei and UV-hot stars ruins the idea that a microwave-bright diffuse dust of electrically neutral atoms or molecules could generate the CMB with its spectral features. You'd have to keep the stars from heating the dust elements, while keeping the dust dense enough to generate the CMB photon-density. How do you preserve that density during expansion?
At the top of the thread you said "the primary proponent of this theory is trying to justify some sort of cyclic model", which doesn't escape this point. (It also didn't lead me to a reference).
However, if instead whoever you are struggling to remember is the proponent of an eternal and static cosmology -- with no expansion, ever -- some of these problems with the idea that the CMB can be the product of cold dust could be overcome. The idea might be that we still have a speed of light lookback, with more distant galaxies being older. The older galaxies being redder could be some sort of dust that is very thick in the distant past, thick enough to completely shroud whole galaxies like a lampshade, turning hot thermal Planck spectra into cold thermal Planck spectra. Then you have to (a) get rid of the dust over time without sending more or hotter photons in our direction, and (b) add spectral features to the cold thermal Planck spectra before it gets to us. I don't see how either could be done without very different atomic and/or gravitational physics than we have in our solar system. Adding in supernovae -- whose light-curves we see redshifted as per the article at the top -- makes this idea even harder, because then you need a lampshade-dust that down-converts photon energies in even more ways.
I'm not aware of any published or even serious attempt to do this, although I didn't look too deeply into the literature beyond confirming that this wasn't something proposed by Jayant Narlikar.