FIXED! I took the pedal apart and noticed that the SD card reader was sitting loosely on the PCB. I secured it against the board using electrical tape, and now it can read both SD cards just fine.
I imagine this is fairly common. When you insert an SD card, it hangs about 4 mm outside of the enclosure. It’d be all too easy to catch it on something and rip the reader out out of the PCB.
If anyone is having a similar issue (i.e., you know the card is correctly formatted but it’s still not being recognized), it’s worth taking a look inside, especially if you bought it secondhand like I did. It’s simple enough, 12 screws (the last one is hidden in the wheel area) and 7 hex nuts (around the ¼" jacks).