Applications :: Moving Individual Song Files Within ITunes?

I keep my iTunes Media folder on my external drive, but I found that recently iTunes has put several of the albums I've ripped on my local drive (/Users/<me>/Music/iTunes/iTunes Music, I assume that's the default location). Not sure why, though I know there was a time when my drive was inaccessible for some reason, so perhaps I ripped them then. Anyway, point is I want to move them to the external drive where the rest of my music lives. I tried just "moving" them in Finder, and I say "moving" because Finder doesn't really let me move but rather copies to the external drive. Which I think is part of the problem, since I then moved the local versions to the trash bin, from which they still played on iTunes. I guess iTunes (or MacOS in general) tracks where files move. Once I emptied the trash, though, iTunes claims it can't find them. Even though shiny new copies are right there in my iTunes media folder on the external drive.