Eureka! Thanks Digital Angel...that was it! I knew it was some kind of newbie problem.
When I loaded ST3, I left the "Force MIDI channel = None" option alone, since it was the default and I didn't want to mess with too many options right away.
But after reading your note, I went back and set it to "Force MIDI channel = 1" and made sure that I loaded my ST3 instrument in part 1...and that fixed it. Duh! After that I was able to assign ST3 to each track in the song and have it play back properly.
I notice that each track I assign ST3 to loads its own copy of ST3. Is it possible to load a single copy, assign each ST3 instrument to a different part, and then assign each BiaB track to the associated ST3 part?