I guess as a reader of this thread I'd like to find out more detail.
- Why did AA cancel the itinerary? Was in a 737 Max issue? A problem with the acceptance of payment by AMEX? In my experience when AA cancels a flight they ask the passengers to call in and they will reaccommodate. Rarely do they do all the legwork for you to get a refund of your booking. We've all seen the threads about the need to manually cancel then head to the Refunds webpage to enter all the info to even start the refund process.
- Reaccommodate. AA is also pretty good at making room on any of their flights without any further exchange of money if there is a schedule or equipment change. This goes back to the first question, why was the itinerary cancelled? If an agent requested $600 more to put you on a different flight because of their own schedule problem then you probably just got a bad agent. They have a lot of latitude when it comes to rebookings due to their own issues when they contact revenue management.
My advice - find out why the booking was cancelled.
- if AA did it then depending on the reason, you should ask AA for compensation if they refused to reaccomodate you in a 1:1 exchange - and should not have asked for more money. If they gave you options and you refused them for whatever reason then that is different. They tried and you declined.
- Again it's not clear why a whole itinerary can be arbitrarily cancelled and AMEX Travel who supposedly is your travel agent didn't contact you. If you truly believe that there was a change in your itinerary that you were not notified then escalate the issue to AMEX Corporate for them to investigate after you've checked your junkmail folders to make sure you didn't miss anything.
- Only after that investigation is complete - if they can't prove that they sent you any notice - should you go after AMEX for their mess up.
But to be honest there is not enough information to fully explain what went on here and even if it is someone's fault - who to lay the primary blame.