I don’t use travel insurance so I’m not sure how they would handle a health event cancellation like this one but I do know from previous experience, AA is pretty inflexible with refunding a trip cancelled by the passenger on a non refundable ticket. I don’t believe JAL will be helpful. I’d pursue the travel insurance option and if that doesn’t work out, I’d phone AA although they will probably only allow you to reschedule to fly up until one year from the date when you were originally ticketed but mention your reason for cancelling and perhaps AA wIll make an exception. Good luck with everything.