HarryT's steps is exactly my process, I sort by date to find the newest book added. But opening K4PC at all really pushes my need to organize things neatly out the window.
I'll have to try setting Calibre to auto-download anything new from that folder as booklover6 said, I didn't know Calibre was capable of doing that.
I might try de-registering as DuckieTigger said, but it sounds like within a few months it'll be a royal mess again on its own.
I'll just have to suck it up and learn to ignore the messy clutter in K4PC.
Thanks everyone for the suggestions.