Thanks much for the help, Ben. Things are working again.
Holding down the two buttons on power-on did make the bootloader screen reappear, so you were right: it wasn't bricked.
On Linux 14.04, I'm running Arduino 1.6.12 with the Arduino SAMD boards 1.6.7, newly updated TinyCircuits SAMD 1.0.5, and 1.1.0 of the TinyScreen library.
This time, I was able to compile the revised version of ArcadeMenu. When I power it on and hold the two buttons, the "TinyArcade Bootloader Mode" screen appears and the TinyScreen+ (/dev/ttyACM0 for me) port appears. I'm able to flash the firmware.
The games that were originally there don't seem to be there anymore, but now the SD card works as advertised (i.e., I unzipped the collection, wrote them on a newly formatted SD card, and now I'm able to select and play a game.