Thank SO MUCH to everyone for the super helpful info.

Carol's pointer to the AA thread on SXM forum has some great ideas. It was the longest thread I've ever seen! I am encouraged to see that some AA customers got refunds, even though the tickets were non-refundable. People had many different situations/dates, and different experiences with AA CSRs. Many people were told the same thing as we were.

I've only called 3 times so far and will continue to call. I am always very polite and nice to the people on the phone.

We purchased the tickets on our Citicards Advantage MC. Thanks for the idea about calling them. I read that one person called them and was able to get a refund. I will try that too.

We were booked at Peter Island Resort. We are landlubbers, not boaters
Peter Island emailed us several days after Irma to cancel our reservation and say they were going to refund us the entire amount.

Glad you pointed out that trip insurance could potentially cover this situation. For our next trip, I will carefully read through all the language.