The dispute will be pretty cut-and-dry - the transactions on my credit card show the associated document numbers and I have the receipt from American that shows the lower price.

I will probably write a note to customer service, and if I have no satisfactory resolution by the time I return from my trip, will launch a dispute with the credit card company. Definitely won't launch the dispute before my trip, luckily i'm only flying AA one way so it won't mess with my itinerary much.

Will update this thread once I have something to report.