In BB 4.1.6, you can switch to a part while stopped without starting that part, it is possible to, pause+end the song and then send a transition command to start the BeatBuddy in the correct part without playing a transition into it. This could all be done on a single button making use of press/release and maybe even toggle features on the MIDI Maestro
For example using one button send:
CC:111 value 1 for pause
CC:115 value 1 for outro, which if Aeros is set correctly the outro command will stop the Aeros without playing the outro while paused
CC:113 value x for the song part, CC:0 will start it from stopped