Do you just re-upload the AccelStepper library + commands each time you want one of the motors to do something?
No. You can get the "what to do" information from the serial port, as dxw00d points out.
Is there a way to configure AccelStepper to loop on the Arduino, listening for USB commands, and then execute them
Maybe, but that is not the intent of that library. The listen to the serial port part should be part of the sketch, not the library.
Or would you use another library completely that is designed just for this sort of thing?
Yes. The HardwareSerial class (implemented as Serial) is what you need.