I don't think a judge would order arbitration simply because (if worse came to worse) the two of you could self-represent and go to trial through regular court process.
I believe that "binding" arbitration requires that two people make a commitment that the arbitrator's decision is, indeed, binding. Non-binding arbitration IMO is merely expensive case conferencing.
She is under no obligation to respond to your offers. Usually well-written offers have a respond-by date in them or they become null and void at the commencement of trial. Offer to settle would come into play if/when determining costs after trial.
Edit - if the date came and went for her to accept offer - you have your answer.
So you now have to measure your offer with the cost of going to trial. You may have to up your offer to get her to bite.
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