Gareth, I don't have any screenshots to post. The way I figured out the problem was resolved was by removing the records from Joomla's Redirect function--they haven't reappeared.
I would be willing to bet that mis-configuring the path to the site would cause issues, but I'd rather just leave it at conjecture and not mess my site up again.
Thanks again, everyone, for the quick replies. It's the kind of reassurance that one needs when embarking on a new undertaking!