Thanks for your in-depth explanations. I´m learning!
Although I’m a molecular spectroscopist by background I am emphatically NOT an astrophysicist. You (personally, not the generic “you”‘) can´t resolve the rotational and any hyperfine substructure of the molecular bands, which is where I cut my teeth. Not entirely sure that anyone can. Betelegeuse is bright enough for spectral resolutions of 100K-1M (my doctoral work was at a resolution of around 300,000) but do the physical conditions in the star’s atmosphere allow that kind of line resolution? That was a rhetorical question. I would be delighted to learn that rotational structure is readily observable, not least because the effective temperature of any species in question could then be nailed down to a very few Kelvin.
Roughly half my DPhil thesis concerned the rotational structure in the spectrum of CeO at ~2300K. Its spectrum is mind-bogglingly complex for such a simple diatomic molecule. There are at least eight low-lying electronic states with populations high enough to exhibit absorption spectra at 2300K. Well over 100K lines in the absorption spectrum between 300nm and 1200nm were measurable with 1980´s technology. CeO is also known to be an atmospheric constituent of a number of cool stars.