You can try travelocity.

Put in the city pair you want to fly, but click any date instead of specific dates. When the rates come up, click on American, then on the calendars that come up pice your departure and return date.

It's easier then playing around with the dates and times at the airline site for the lowest price, then you can book it there or take the information back to the other site and get the bonus miles. I don't think you will get an airfare as low as you are trying to get though.