Just wanted to report back as OP since the trip is now over. I ended up calling AA and the agent was awesome and put us on MUCH better flights that were close to the times we originally booked. She said we'd automatically be refunded the seat fees we'd paid for, but it's been about two weeks and that's yet to happen. Still could, but just in case I took the extra step of using the refunds request page on AA.com. It's a little convoluted, but here's what I did:

1. Find your ticket number in the original confirmation email (each passenger will have their own).
2. Go to the "Receipts" page on AA and enter your ticket number and last name.
3. Click "details" and you should see two separate transactions: the original ticket purchase and the seat fees. The seat purchase will have its own "ticket number" that's different than the flights.
4. Go to the refunds request page at AA.com and enter that new ticket number and your last name. You'll need to do all this separately for each passenger, but that page did find each seat purchase using the unique numbers. Go through the steps to submit a refund request.

Hopefully this works and helps somebody out in the future!