I understand your broader message about pedagogicality and not causing confusion. I agree there is no simple Doppler formula for cosmological redshift, but I read Bunn & Hogg to say that there is a specific mathematical approach to solving it, which involves parallel transport of the velocity four-vector along the light path by integrating a large series of tiny SR Doppler redshifts. That's what their Fig. 3 illustrates. They say:
"Imagine many comoving observers stationed along the line from the observed galaxy to the observer. Each observer has a local reference frame in which special relativity can be taken to apply, and the observers are close enough together that each one lies in within the local frame of his neighbor. Observer number 1, who is located near the original galaxy, measures its speed v1 relative to him and gives this information to observer 2. Observer 2 measures the speed u of observer 1 relative to him, adds this to the speed of the galaxy relative to observer 1 using the usual special-relativistic formula, [equation 5] and interprets the result as the speed of the galaxy relative to him. He passes this information on to the next observer, who follows the same procedure, as does each subsequent observer. At each stage, the velocity of the original galaxy relative to the observer will match the redshift of the galaxy in accordance with equation (4)."
[Equation 4 is the SR Doppler redshift formula.]
I think their mathematical approach (above) is wrong. As I explained in my first post, relativistic Doppler redshift incorporates an element of SR time dilation. But SR time dilation is not possible as between privileged emitters and observers who exactly comove with the local Hubble flow. Without SR time dilation, SR Doppler redshift is nothing but classical Doppler redshift. We know definitely that the latter by itself is not the solution to cosmological redshift.
Do you agree with my assessment of their approach?