Tiramisu,
whilst I respect you and your moderate colleagues, (HiF, JSL, GG etc), what you suggest would only work if Bassa want to do it.
The evidence that I see is that they do not want to do it.
It is just about Power for them.
In which case, BA's only option is to break their power.
There are lots of ways of breaking their power, but the obvious one, which has been very common in the UK - Shell, ICI, Unilever, BP amongst others have used it - is to give the 90 days notice and to ask EVERY BA CC member to re-apply for thier job.
I've worked through this, and I hated it, but it provides the sort of solution that BA currently need.