Moved from Tarantula Hawks.

In the key in Hurd(1), the first couplet separates females (antennae distinctly curled) from males (antennae relatively straight). And directly after that, P. formosa(= grossa) is immediately separated out by the key characters:

"Anterior femora below clothed with very long, bristle-like hairs, middle and hind femora glabrous or nearly so; middle and hind tibiae without anterolateral or posterolateral longitudinal groove."
The above image clearly shows the long hairs on the anterior femur...and it's clear from the full-size version of your 2nd image in this series that the hind femora are glabrous. Moreover, going through the key in Vardy(2) also leads unequivocally to P. grossa here. In particular, Vardy's last couplet (#10 on pg. 53 of Part 2) leading to P. grossa states:

"Spines of hind tibia distinctly higher than teeth (fig. 186)"
And comparing his "fig. 186" (on pg. 48 of Part 2) with the full-size version of the 1st image in your series here clearly verifies the "spines longer than teeth" character. And other aspects of the detailed species descriptions for P. grossa in Hurd and Vardy match up well too.

So that clinches the ID here, and I'll move these posts to P. grossa.

PS: I'm also hoping you'll get a chance to post further images for the other Pepsis your cousin found, showing some of the characters that I mentioned would confirm the putative ID of P. chrysothemis there: