Unfortunately, this is unlikely to succeed. The court, especially under Roberts who is a fan of arbitration, has ruled in favor of arbitration clauses recently.
I think I read that in the giant investigative piece about arbitration in the NYT.
> One of the players behind the scenes, The Times found, was John G. Roberts Jr., who as a private lawyer representing Discover Bank unsuccessfully petitioned the Supreme Court to hear a case involving class-action bans. By the time the Supreme Court handed down its favorable decisions, he was the chief justice.
The Republican members are there to represent management.