The only key I know of for nearctic Polybiomyia is Shannon(1925)...written before P. reinardii was described. It would be great to know if there are more recent keys!

The female AZ post here, as well as the nearly identical male from the same general area below:

   

...both look quite different from the other current TX posts of P. bellardi:

     

The latter are in excellent agreement with the key & description of P. bellardi in Shannon(1925), which was based on specimens collected in TX...and P. bellardi is also listed as having range "Tex." in Stone(1)(1965), and in this 2005 Systema Dipterorum record.

I wanted to understand this situation better, so I very carefully read Hull's 1930 original description of the female P. reinhardi (on the 3rd page of the PDF here)...cross-referencing the many details there, sentence-by-sentence, with the female in the 4 photos of this post. While some characters seemed nicely compatible with the photos here, many more were not! [Rather than list those details here, I invite you to carefully reconcile the description and photos...I trust you'll see what I mean.] Of course populations can vary within a species, and authors can sometimes be inaccurate in their writing...but, even accounting for that, the degree of discrepancy seemed too large for me to have confidence in an ID of P. reinhardi here.

It then occurred to me that perhaps this female might fit better with the other "new" species, P. festiva, that was described in Hull(1930). Pursuing this, again a number of characters fit well...especially for the head (e.g. reddish medial & lateral stripes on face, w/ black spot below eye, etc.). But may others (e.g. various yellow spots on the pleura) were way off. And both species were described by Hull as having reddish posterior bands on the abdominal terga...whereas those bands are clearly yellow here, as is typical for most species of Polybiomyia.

As you noted, P. reinhardi has been synonymized under P. bellardi (see here); while P. festiva has been synonymized under P. townsendi (see here)...though, as is often the case, it's not clear who established the synonymies or on what basis (they were still listed as separate species in Stone(1)(1965)). Note that each of bellardi, reinhardi, and festiva were described from TX specimens, and Texas was given as the range for each in Stone(1)(1965)...whereas the range given for P. townsendi was: "N. Mex.; Calif., Ariz., Tex." (see also here).

Given the descriptions and the location here, if one were to require an ID based on described species...I'd reluctantly go with P. festiva = P. townsendi as my best choice among the options, though none really fits well enough. As far as I know, there's been no published revision/review of nearactic taxa of Polybiomyia since Shannon(1925), and my best hypothesis is that the female here (along with the male in the first thumbnail above) belong to a currently undescribed species.

Wing looks like Syrphidae to me.