For some reason, pk3DS didn't "spit out" any files for me, it just changed the files already in the romfs file. A LayeredFS directory is only supposed to contain the data that has been changed. Do I need to use one of the "Rebuild" options?
Note: I don't want to put a gigabyte or more data on my SD card, as LayeredFS files are only supposed to be a couple dozen megabytes.
Edit: if you go to Options → About GARCs you can see in what file each piece of data is stored, and copy only that exact pathway.