So, very interesting precedent being potentially set here and avenue of recourse against PayPal for banning and unpersonning users. Can Gavin and his backers file for arbitration against PayPal in which the company would have to bear the cost of arbitration fees pursuant to California Law?

Patreon would actually have to cover the fees in advance. Unless the judge reverses himself, Patreon's motion for injunctive relief will be blocked which will force arbitration action. Potentially MAJOR implications may result from this court filing and it does not look good for Patreon. This is a serious way to fight back against the tech cartel (i.e. PayPal, Mastercard, YouTube, Patreon, Facebook, Twitter, etc.)

Source: https://youtu.be/5Vr4pbVgjEs

Tldr: Gavin and his backers could retain a lawyer and file for arbitration against PayPal. PayPal would have to bear the cost up front pursuant to California Law as a result of this court filing against Patreon. Judge presumably will force arbitration. This is a way to fight against Gavin's PayPal banning