Well, that was easier than I thought! I found three banknote engravings that may have been based on your illustration by Ostrander Smith. All of these are from the USPS Commemorative Panel series, which is a terrific library of intaglio vignettes and portraits by American Bank Note Co. and other banknote companies.
The first one almost certainly used your drawing as a model, however, it was done by Jeffries Bank Note Co. and would have to have been engraved much later, probably in the 1940s or '50s. It's a mirror image, so the engraver was working from the original art, since the engraved plate prints in reverse.
The other two are both by ABNCo. These may have used aspects of the drawing, like the Phrygian cap, but they are considerably different. The first one was created at least as early as 1929, maybe earlier. The second is probably from the 1940s. It's also possible these were modeled on entirely different illustrations.
I'm not sure who the engravers were on any of these. I'll look through the rest of my collection and see if anything else turns up.