We had an almost identical situation but unfortunately I did not have much luck with AA. I followed the exact same protocol, and explained our situation very carefully; we even have mitigating circumstances that will make rescheduling to later in the year or next year impossible. But no dice from AA.

All I was "offered" was a travel voucher for the value of the flights (which is standard procedure when you cancel a non-refundable reservation anyway). I also got a condescending reminder from them that "non-refundable means non-refundable." Yes, that's a quote from AA's response.

So it seems like it may depend on whom you get answering the email.