> The image isn't enough to demonstrate the difference...
Precisely.
> ...But the speed of light is, along with the way acceleration and redshift work.
Are you referring to the cosmological component of redshift? I suppose that, at least in principle, we could determine the cosmological component by first measuring the Hubble constant from the change in distance, over time, of those stars whose distance can be measured without any assumptions about redshift, but has that actually been done? (or some other experiment that directly calculates the cosmological component of redshift?) OP's claim is that we already have sufficient experimental results, not that we could, in principle, get them. AFAIK, experimental error in these stellar distance measurements is too large, and they are over too short a period of time, for the rate of expansion of the universe to be taken directly from them (note that the anomaly that is the subject of the article itself brings into question the accuracy of the cosmic distance ladder.)
> A chain of logic that starts with the evidence we have, goes on to what telescopes show elsewhere, and then concludes about expansion, is not circular.
It seems pretty clear that OP was thinking that if we were to observe the universe from a distant galaxy, it also would seem to be at the center of the expansion - but that would be the case in both scenarios, so it does not actually distinguish between them. If, however, OP had in mind some other set of measurements that, when combined with those from Earth, distinguish between the scenarios, then the question becomes, can you deduce what those far-away measurements would be without choosing between the two scenarios, either explicitly or implicitly? If that choice is being made, then you are begging the question. What set of measurements and calculation do you have in mind that avoid this circularity? (the above-mentioned redshift measurements are a separate issue, both because they are clearly not what OP had in mind, and because they do not depend on any calculation of what observations would be made from a distant galaxy.)