The OP's letter and the deposit of the 3000 miles have nothing to do with each other. Customer Relations determines the compensation for delayed flights (within AA's control) and all passengers on such flight then receive the same compensation. Having suffered through two mechanical delays in excess of three hours in and out of EWR since September, I've had 3000 and 4000 miles deposited in my account respectively. Since miles are not as important to me as the 500-miles stickers, I often will speak to Customer Relations and ask that they give me the appropriate 500-miles stickers instead. Each time they have obliged.

As for SqaureDanceGuy's assertion that letters to AA are seldom read by humans, my experience has not been the same. Ironically it is the compliment letters that rarely receive a response, but a complaint letter most always receives a response even if it is via a form letter.