There’s an easy solution: the airline automatically owes the maximum amount. This would save everyone much time and put some burden back with the airliner (by potentially paying more than the customer had, though at around USD 1800 it should be quite even, especially once you consider the time spent to get your money back)

You already need to insure higher values anyway if you want to be entitled to a reimbursement, so this would set a nice minimum that encourages customer friendly behavior.