So after several months of hesitation, I bought a mod kit for my cabinet, and got it all hooked up after several hours of struggling and/or fretting:
It initially worked great. Then I got the bright idea to run the system update prior to moving the cabinet back in place, and now the audio doesn't come out of the speakers.
I suspect it might be because the audio output no longer shows HDMI as an option. I still get audio directly from the Pi, but when I plug the headphones into the board, I'm only getting static.
Is it something with the software, or could it be the hardware? I doubt it's the hardware, since the HDMI output is still working.
And if it is the audio output setting, how can I fix it? It's based on Batocera, though I have no idea how to connect it up to a computer to check those things.
The SD card seems pretty firmly set in place, and the instructions advise against removing it.