Of course I spent much more time than I originally imagined but the project was fun, taught me a few things about ST's tools and Chinese clone chips, and left me with some new business cards to hand out.  I've given away two and the recipients were both amused so that's a success.

I've also learned a few things that I will address if I ever revisit this project.

1. I'll add a ground pour on the top layer of the PCB.  I didn't originally because I wanted to minimize thickness but my 0.6mm PCBs suffer from a slight warping that I think is due to the ground pour on the bottom of the PCB.
2. I'll look into an open-source USB stack like Dmitry Filimonchuk's libusb_stm32 or Ha Thach's tinyusb as well as a command-line only development environment to get away from any restrictions on distributing the full source code and compiled binaries.
3. I'll redo my graphic to fit in the empty space on top of the PCB so that all the text on the top PCB is visible.

I hope anyone who's spent time reading has enjoyed this project.