[dfwgirl]

So, first let's discuss your bag size. If it slides into the sizer, really it is no problem. YES, bigger bags fit, however remember the "Shared Space" announcement. Your giant bag takes up some other passenger bags space. Second, very wrong for the agent not to give name as requested. Employee numbers and last name are not given out to protect the saftey of the employee. All management can see what agents worked the flight. First name, or even general description is fine. Flight crew does not know the name of the agents working the flight.
I have seen that baggage abuse has gotten so bad that agents are taking pics of bags, in case as dispute comes up. On the other hand, agents are human. If a bag is in question, should it be so challenging to slide it in the sizer?? If it fits, it goes. Why is that a problem??

Your class of service, first or main, does not matter to the bag regulations. FAA fines AA equally for excess/oversize. If you travel $40,000 per year, you should know what size carryon to bring to the airport.