UPDATE: Thanks to NiLuJe for making me re-visit one step in my process. So I just took a file that was converted, and all I did was use the MobiMetaEdit program to change its ASIN to the Amazon number, and turned off Airplane Mode, and the Kindle downloaded the art for me! The steps just got a lot easier! Thanks!
-All you need do is change the ASIN parameter in the file.
-You do not need to load the thumbnail or format the filename of the book itself to include the ASIN.
-You still likely need to clear old metadata if you sideloaded books before this ASIN change. I think this is what was stopping my Kindle from downloading information when I tried this before.
-The number you put in the ASIN field, as far as I can tell, must begin with a B. You cannot use an ISBN-10 or ISBN-13. I tried on one book, at least. So what that means is if you have a book that is not on Kindle yet (one book I have is an old Xanth novel that was scanned in that's not available in Kindle format yet, so it doesn't have an ASIN yet), you have to manually load the thumbnails, yourself.
In any case, thanks again for the clarification! Makes the Calibre modification easier, I would think!