can i send in my evidence and witness list for filing in washington superior court for an arbitration case?

I suggest you call the person assigned to your case and ask.In most states your adversary has to agree with the arrangement. You may have to submit an affidavit as to why 2 trips to WA are too much for you.
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LEGAL DISCLAIMER
Mr. Sarno is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Sarno strongly advises the questioner to confer with an attorney in their own state to acquire more information.