My reading of what you have written is that AA stuffed up. I don't see what exactly you expect CX to do when you turn up an hour or two before a flight that is already fully booked. The only way you could have flown would have been if someone else was kicked out so what makes you think you have the right to do that? Even as a CX Diamond I have to give them 24 hours notice to do that, and only then (in J) on a full fare ticket.

Take this up with AA (assuming that is who you made your reservation with).