Over the past few days I've had several schedule changes from American Airlines for early- to mid-2022, some very significant and inconvenient (including an overnight flight from LAS to PHL followed by a 14-hour wait for my TATL).
In every case, I've managed to get straight through to AA Customer Service with no wait whatsoever and have had a very helpful and patient agent who has rebooked according to my wishes and even managed to increase the TPs earned.
I get the impression that the agents are so busy at the moment that if you have done your prior research and simply present them with flight numbers you would like to be rebooked onto then they are happy to do it without fuss. Otherwise you're going to have to repeatedly explain that you
really don't want to be routed through DFW or ORD.