Very good observation. I lot of my time shooting was having them incrementally adjust their instruments so as to not have big reflections. And since it was a 3'x4' soft box, and a lot of curved surfaces, there was some considerable "cheating" going on, as in "cheat that mandolin a little more to the left". The acoustic bass was also a problem and it was cheated a LOT to avoid reflections. That's the second band I've photographed that bass in, and in both instances, it photographs amazingly well.
Jodo - the "cheating" as it were, is just putting the mantra that was pounded, I mean hammered, into us pretty much on a daily basis at Art Center College of Design - "The angle of incidence equals the angle of reflectance" That's about all you need to know when dealing with reflections.