While it may have been an error on your part, the fact remains that you booked a ticket in violation of AA's Contract (a so-called "impossible" booking) because you had not yet cancelled the first reservation.
AA has particularly strong "sniffer" software to guard against inventory spoilage and you are an unfortunately caught up in that.
There is nothing you can do to force AA's hand here and you have already rebooked.
Now that you have a positive booking, why not call AA back and ask if they might help you out. Agents can no longer call inventory/revenue management to open space, but a supervisor can send a message. It may take some time and it has a very slim chance of succeeding, but it is worth a try.