I appreciate your wisdom Diki! Since I had no intention of ever playing the tracks that I muted, I just went into Style Composer and deleted the content. Then I used Makeup Tools to tame the bass level so that I can run "100" level with all tracks on. Now when I select another style everything plays as I would expect.
I already knew about designating tracks for Track Mute. But I would have never thought to look in the DBeam as a way of muting parts! I don't really do very much with the DBeam. Perhaps it's the lighting in my dining room, but I've always found it hard to get a consistent response.
Re: muting parts via MIDI... in a general way, can you please describe how this is done? (I assume that you're referring to STYLE parts, and not Upper 1 & 2, Lower, etc.) Because the BK-9 has sliders, I probably wouldn't use external gear with it. But being able to toggle the tracks individually on the BK-5 and BK-7m might come in handy. Thanks again for your help!!