I agree with you; you can't build up a perfect blackbody spectrum by superposing different near-blackbody spectra, and that led to the cosmological thermalization problem. Furthermore, baryonic intergalactic dust isn't like dark matter: we see redshifted spectral features of components of such dusts imprinted on all sorts of backgrounds from quasars to the CMB. The dusts tend to be greybodies. (I'm ignoring the warm-hot intergalactic medium here).
The CMB has narrow spectral lines imposed on it by galaxies, dust clouds, and similar objects. Those lines can be used to measure the CMB effective temperature at an object's redshift. A specific example of how this works is linked at the bottom of this comment. If a similar highly dusty object is found in the foreground of a bright quasar (merely nearby quasars were used in the case below), we could get an even tighter measurement of the CMB effective temperature at the dust, and perhaps look in new ways at how the CMB deviated (at the dusty object) very slightly from a blackbody spectrum. This amounts to a new line of evidence in the study of the expansion history.
More generally, constraining the evolution of the CMB temperature in the matter-dominated era (T_cmb > 4 K, z > ~ 0.4) will prove fatal to ideas like some in this thread (which is already in trouble because of other spectroscopy e.g. the Lyman-alpha forest and Gunn-Peterson trough).
I don't really understand the summary of the "'fringe' theory" at the top of the thread (and I can't identify which specific theory throwawaymaths means). I guess the idea could be that some unknown mechanism might homogenize the emissive components of baryonic intergalactic dust but not circumgalactic medium spectral features. I suppose one could try to investigate a non-adiabatic expansion to explain those features found in the CMB in a nonstandard way. Non-adiabatic components in the expansion have been examined by various theoretical teams in the context of quantum cosmology and/or "fifth force" dark energy, although mostly at much larger lookback times than the the standard surface of last scattering.
I don't understand what was meant by '"longer" (aka galactic expansion) timeframe'.
Finally, "echo of the big bang" isn't really helpful in understanding the origin of the CMB photons, why they're now filling space with a thermal Planck spectrum, and why we detect small variations in that spectrum in narrow views along different directions, but like "fabric of spacetime" I guess we're kinda stuck with the expression.
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(Open Access) Riechers, D.A., Weiss, A., Walter, F. et al. Microwave background temperature at a redshift of 6.34 from H2O absorption. Nature 602, 58–62 (2022). https://doi.org/10.1038/s41586-021-04294-5