They are much more delicate than a lot of people understand. Just because you don't still see overt aggression from the tang, it is quite likely still being intimidated and stressed out by the tang.
Also, I highly doubt that the CBB is satiated from picking at the rocks. Many many of them come in super stressed, thin, and not eating much. If it looks thin at all, I would assume that it needs more than it's getting. It might get a little expensive, but fresh cracked little neck clams might work to fatten it up and keep it from starving. I nursed a CBB for about a year on little necks, then one day it decided to take frozen mysis and never looked back. Kind of drastic, but a LOT of these fish starve....