If you are going to write a complaint, you will need to be very brief and to the point. I would recommend cutting the verbiage by 90%, using bullet points, and sticking to verifiable facts.
Having said that, unlike some of the "nightmare" threads we get here, you do seem to have been not well-treated (to put it mildly). If the facts are as you report, IMO you are definitely owed an apology and some compensation.
Do you have any status with AA? That could smooth your path a little.