Totally applaud the ballot, you should vote YES on moral, ethical, common sense and career future terms.
[One other point is that if you DON'T, your CC will have no credibility for the foreseeable future, and your management will run rampant, crowing, saying
'I told you so'
imposing even worse conditions knowing they can get away with them, and generally pushing the bat in even further.]
Once you start in a game of high stakes poker, you cannot flinch - it helps a lot knowing that your opponent has blinked first and subsequently folded on every single other game they have ever played! The incompetence shown by BACX management has continued in that they have allowed your CC to pick a fight at a time and place of the CC's choosing, and on a subject where the management are clearly one hunnerd persent in the wrong.
You cannot lose, it is a no-brainer (like your management).