Unfortunately, not really!
The BeatBuddy is not as versatile as the Aeros is as a MIDI receiver/slave. The BeatBuddy needs the Start command from the Aeros to start and stay in time as it plays back
Using version 4.1.6, you could potentially not need to use the Start command, in this version the Aeros will start the BeatBuddy on time if it transitions to another part while the BeatBuddy is stopped if that part exists on the BeatBuddy.
So, you can disable the Start command from being sent by the Aeros when it starts playback/recording. Then, when you switch to part 2, the BeatBuddy will start playback on part 2 in time with the Aeros.
Let me know if this works for you!