First, welcome to Flyertalk.
Second, there is actually an American Airlines Forum where you might find more specific support.
I am happy to hear that you are safe... I think that is the most important issue here. It sounds like you had a crew that performed very well.... you might want to send a note to AA recognizing their efforts.
I do not believe that AA has any more mechanical problems than any other major airline. Realize that every time a flight is late or cancelled, it causes ripple effects throughout the system... airlines do not have spare planes and crews sitting around waiting to be called into action. And, no one would willingly fly planes that were knowingly unsafe. Seems like you just happen to hit an unlucky stretch.
I would expect that AA is working on some compensation... but if you want to push it, you should send a note to AA Customer Service... their email address is on their website... and detail your concerns and inconvenience. You will probably receive a voucher for future travel.
Do contribute to FT!