It turns out that the serial programmer wasn’t working earlier because I was using it with a USB-Serial adapter, as I feared. However, when I dug out an old Sony laptop with a real serial port, it worked right away.
The PETdisk has most of the necessary connections for reprogramming brought out to the socket used by the SD card adapter, so it should be simple enough to connect a programmer to update the firmware. I will try this soon and let you know how it goes.
Also looking into AVR bootloaders so in the future the PETdisk firmware can be upgraded by just putting a file on the SD card.. watch for that also.