Thanks for the response, Chaley.
I've done a tcpdump on my connection in to my server, and you are very much correct - Calibre Sync is talking to the content server to do the navigation within the android app.
I'd not done any googling on running Calibre headless, your mention of xvfb helps a lot, getting me to threads like
https://www.mobileread.com/forums/sho...t=97841&page=2
It sounds like my use case is fairly niche for the general user population of Calibre, so I'll pursue the xvfb option, as I do very much want to be able to run Calibre headless (I'll be killing the process and firing it up in the GUI if/when I need to do some advanced library management).
As an FYI - the benefit of all of this: I'm running this on a VM on a small home microserver, along with a variety of other headless services. I want to be able to drop and restart this VM without having to worry about logging into a GUI to fire up various apps.