GaN & SiC piezoelectricity problematic?
I imagine the actual answer may depend on the transistors you're interested in.

For example, there's no "oxide layer" in a typical GaN-on-SiC HEMT; the gate forms a Schottky contact and the device is a "planar" device with a 2DEG. Piezoelectricity has little effect here since there is little potential across the crystal (only along the surface). Incidentally, typical SiC substrates are semi-insulating, so there's no electrical contact on the back-side of the GaN, either. Without the second electrical contact, you won't get any piezo-related effects.