I just tested this out on my gba sp. I think sounds not overlapping is fine, because in general this is like beatboxing, where you're just creating a cool simple rhythm, the space between is most important.
I think in your shoes I would have also gone the route you did where directional keys modify, that's the most elegant and pleasing, but after testing this out I think Bass snare on BA, and then symbols and toms on the d-pad would be more fun and kinetic for creating cool beats.
As usual, a really cool bit of design, I am yet to dislike a release of yours. I wish more game designers were as committed to designing something interesting as you are.