Took some research, but this video was the key:
BetaFlight binaries are now compressed into a single archive with all targets. You need to get that larger zip file from Github in order to get the CC3D bin file.
Take advantage of LibrePilot being able to flash a binary without using boot pads, in order to flash the BetaFlight bin file.
Lastly, when connecting to BetaFlight afterwards, you must power the CC3D before connecting to the configurator. I used a 1S battery connected directly to the + and – pins in the bank of pins for ESC signal wires.