First of all, THANK YOU SO MUCH for taking the time to help me.
Now.. indeed, my Kindle does have both a Rothfuss, Patrick folder and a The Name of the Wind_ The Kingkiller Chronicle_ Day One_B0010SKUYM.sdr folder... I merged the .sdr folder that was inside /Rothfuss, Patrick (I saw only 2 files inside it) with the correctly named one and... nothing. Still no cover.
So, just to be sure, are we 100% certain that it's possible to take a DRMed AZW3 file, change its cover, and not lose any of the features that come with DRM? Because if you guys do this regularly then I'm being thick and I may need more step-by-step instructions
Edit: Wait, is the cover one of the things that are saved in the .sdr folder? Because I don't find that particular file/shortcut there...