EDIT: While this did make the sync icon usable again, it has not been successful in actually synching my books across devices. My K3 and K4PC both think they are at the furthest page read, even though my iPhone is well beyond them both. Not sure what to do at this point. I re-converted the books hoping that would solve the problem, but it didn't.
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Thank you for this!!
In iOS 5.0 (no jailbreak) this worked perfectly. Just had to navigate to apps/com.amazon.Lassen and move them to Library/eBooks. The only thing that threw me off at first was for whatever reason in iExplorer I wasn't being allowed to type in a path name, so I had to use the directory tree on the left. Thanks for the save.