So, if there were to be a legal challenge, what would the likely outcome be? The destruction of the BA MSL? Actually BA would love that, it would kill Bidline stone dead and all other seniority based bidding. So the BMI guys would probably not get those LH commands they want as it would cost BA money they would not need to spend, also they would not get Bidline and the lifestyle improvements it represents. Commands would be at BA's discretion - upgrades could easily become dependent on how good your golf score was when you last played with the Chief Pilot.
All the above is deliberately overdramatic, but when entering into a legal dispute it is important that one has a very clear understanding of where it will take you. Often the only winners are the lawyers and the end result is seldom the panacea being sought.