I had to solder serial Tx, Rx, GPIO0, 3.3V DC, and GND onto test points or convenient pins. Then I had to flash the firmware using a USB-serial adaptor, connected to a Ubuntu 16 VM.
Only after flashing the firmware did the device appear, but it finally does work! I plan to write a blog post about the whole experience, thanking Smile Wang from PCBWay, Pablo2048 from this forum, and Aaron for the help.
I ordered 3 pieces, and all 3 are now working. Now I plan to take pre-orders for a larger batch, a new production run that will be for sale on Tindie and eBay. Please contact me if you'd like the EspUSB Tiny, so I know how many to order!
[1] https://atcnetz.de, YouTube 12002230