To serve strike notice on WW is to cross the Rubicon.
A WW complete win would mean BA Ts&Cs being trampled on for the foreseable future without the option of industrial action. Even if you voted against the action it must be obvious that a comprehensive defeat for the union means game over, bye bye pension, bye bye seniority, hello lower pay. The weak need to realise that in war there is nowhere to hide.
For that simple reason unity is the key. There is no alternative.
Good luck, it is vital for the industry at large that BA pilots stick it out and succeed.
p.s. instead of 'quizzing' and questioning your BALPA reps you should text, email or post your total support to/for them. WW will see it on their faces when they eventually get back to the table.