Despite what everyone says above, books can definitely be on the SD card, because they were showing up fine from the SD card for the main profile.
For my particular issue, the problem apparently was that the Fire keeps a different index of books for each profile, so when I created a new profile, it needed to build a new index of all of the books from scratch, which took a while--when I came back the next day, the books showed up fine in the Books section and I was able to open and read them fine without any special apps.
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