Actually the SOSR 90 day thing is even simpler than persuading the judge that there is no chance of achieving a settlement. All that BA have to do is persuade the judge that they believe there is no chance of achieving a settlement. This is the legal test - there has to be a genuinely held belief, not that that belief is valid.
That said I remain unconvinced BA would do this, I think they will just ignore the strike and take sanctions like ST removal. The last strike was ineffectual and the tactics that worked last time are likely to be used again.