Because this is a reroute due to schedule change, an AA agent can make a change to any available AA seat without regard to the fare bucket used for your ticket or what is available. It does not matter whether you are on AAnytime or the cheapest BE seat available.
Before calling, you should do the research and present the option you want. The easier you make it by providing the date and AA flight number, the easier it is to accomplish this. No need to make a big fuss, all it takes is saying that AA changed the timing and the new timing does not work for you.