Okay, so I partially solved the problem. When the multiple files window pops up, I click the Artwork tab and then UN-check and then RE-check the little checkbox BEHIND the blank square in the upper left, that reads: "drag artwork here or right-click to paste". Then I click SAVE and, in most cases, the Artwork then goes away.
However, there is one album in particular where this doesn't work, AND there's no little checkbox behind the blank square, to un/re-check. STRANGE.
And additionally, even with MusicBee showing (under Artwork view) that everything is blank, when I go to Windows Explorer (Win 7) and use Medium Icons view, many of the little halfopened folder albums there STILL show art.....
Any ideas?
Thanks, all.