I just don't know what more BA can do to try to get crew to understand the facts.
Tricky.
In most other industries the answer would be simple: Allow the management to continue the factual/dignified and respectful path (as exemplified by WW last Wednesday). And, at the same time other employee groups that have contact with the the aggrieved section,(CC), "tell them a few home truths".
In BA the best group to do that would be the pilots. The problem is that the contact that they have tends to be when they are flying aircraft together. Not a good time to deal with highly charged and complex issues without adversley effecting a good team spirit and/or safety.
Even if they so try, I imagine the response would be rather the same as Mandy Rice-Davies remember her? (at the High Court) -
"Well (s)he would say that wouldn't (s)he!"