Way more than most will have you realize.
I do hope you can get an attorney involved. They have created a mess and you have had to spend time, money and stress to sort out their own illegal practices. That deserves to be compensated, IMO.
@LabLady you did a great job! I, for one, wasn't worried. I knew you had it in the bag when I read their pitiful, nonsense response that cited no authority for their awful arguments.
I would get a copy of the court's order to arbitrate signed by the judge and email that to JAMS.
Since the court did not dismiss with prejudice, when this gets to a settlement negotiation point because they don't want to pay for JAMS, I would want to make sure that a mutual walk away settlement includes language that says I am released of all liability concerning this account. That will mean no one else can come after you in the future and that the alleged debt is gone for good.