A shallow drum can sound very deep. Just check out the Modern Drummer video demo of the 4x15 Beier steel snare drum. I have recorded using a shallow maple Pearl free floater (what are they, 3.5" deep?) at a medium low tension, and while it wasn't the lowest pitched snare sound, it was very big, fat, and powerful sounding. I've never tried a low tuning on a true piccolo (3×13), but I imagine it would sound pretty similar to the free floater sound I referred to.