I now only transport the heads in the upright position. I once laid one on it's back and the vibration rubbed paint off the BG where it contacted the backboard.

I honestly don't remember which game (it was probably 15 years ago). The problem is that parts loosen over time and shift around allowing contact. There's a reason that they put the protector pads on the backboard. Unfortunately, the pads degrade over time and can cause damage themselves. You could probably transport them this way if you carefully wedged some cardboard to keep the BG from shifting/vibrating, I just prefer to transport them upright.