As nice a program as it is, Picard is really more about retrieving data and artwork from the MusicBrainz database than local edits; cover art, especially, is hard to work with if it’s not coming from online. Unless I’m misreading what you’re trying to do, I’d recommend using MP3Tag (if you’re on Windows, or, apparently, Mac with Wine) or Puddletag (Linux) instead for your own files – both have relatively good handling for embedded art.
One other thing you might try if you want to stick with Picard is re-enabling the “Local Files” cover art provider. It’s not my typical workflow so I can’t really say anything about how or how well that works, but it seems like there’s a chance it does what you want.
All right, apparently there are ways to do this: the “Local Files” provider does search the directory so it should work if you have your image there and named as Picard expects, or you can drag and drop your image file from wherever else it’s saved onto the blank CD icon in the lower right.