When my bag was damaged last year I didn't have time to send it in for repair/replacement, as I had another international trip coming up in two weeks. SFO baggage claim told me to purchase a bag and send in a receipt., and thought I had a pretty good shot at reimbursement. I did that on-line and 21 hours later had a response from AA that they would send me a check for the replacement cost of the same model. Don't know if EXP status factored in there and was surprised they did respond so quickly.
My total cost was $119 so that may have been a factor. It was a Costco/Kirkland rollaboard that I had for years.
Could you buy a bag locally, or on-line, that you can return in the event AA won't cover the cost? I'd probably go in that direction as a start, so you have a replacement receipt to send into AA.