Maybe, lazy or tired light, and everything shifts towards specific spectral lines or frequencies/wavelengths at distant observation. Attenuates? Asymptotes to the hydrogen line?

If light got tired it would make ordinary chemistry impossible. You wouldn't see spectra because atoms themselves would work differently (and probably not at all).

The fact that we can tell that it's hydrogen makes it extremely unlikely that light behaved differently there.

that doesn't work out. from the spectra we're seeing hydrogen spikes red shifted, so the lack of any other spikes is very strong evidence