That got me past the sticking point and automatically pulled/built/installed all the requirements in my local site-lib.
Directly copying the *.egg directories over to the site-lib of my Ignition server didn’t work, but thankfully all the libraries were cleanly implemented in subdirectories of the .egg directories. So I just copied those directories into site-lib on my Ignition server and everything appears to work so far.
Is there a better method to move/install things from site-lib/*.egg on one setup to another?