Okay, nevermind, after noticing the "save to disk" option I wondered what it was for, found
this thread and thus my problem was solved.
Although, I've set the 'author' field to [first name] [last name] and the 'author sort' field to [last name], [first name] (like, the author is Leo Tolstoy, and I've set the sorting field to Tolstoy, Leo), yet the Kindle app sorts by first name. Is this a flaw in the Kindle app or does the author sorting field just not work with it?