Turns out my issue was more insidious than I thought. I discovered that even though Launchbox imported all of my games, none of them were playable, that is, I would click on them, and the game would not launch. So, I copied my MAME folder to my local machine, and re-imported from there. The games are now all playable, however, when I attempt to export my curated collection to a new folder as @JoeViking245 described above, I get 'No ROM files were found to copy to the destination folder'. I've seen some comments around the web that imply that this won't work if you've used the full set importer, but that doesn't seem right.
Edit: I noticed that in the Arcade Platform dialog, the Game media type was not pointing to the correct folder. I've changed it to where the games actually are, we'll see what happens.
Edit2: Same error.