I've solved this problem, and oh boy, do I ever feel silly.

I loaded Metroid Prime - Pinball (a rumble pak compatible game) and checked the in-game options. The option to rumble was grayed out, which instantly led me to believe there was a contact issue with the EZ Flash 3-in-1 slot-2 device. So I took the EZ Flash out, gave it the traditional NES blow of air, reinserted the EZ Flash and ta-da!

Just to confirm this wasn't a fluke, I removed the EZ Flash, and checked my GBA ROM directory. Empty.
Reinserted. All GBA ROMs present.

GBA ROMs are visible with "set file list type" set to NDS, provided there is a slot-2 device inserted.

x)