What's the easiest way to carry 4x8 sheets of 70-lbs drywall by yourself?
The way the GG would damage the drywall is by putting too much torque pressure on a single spot while you're lifting, since the GG is naturally going to want to twist the panel at the point it grips, given the way you have to hold it.

You probably can protect the drywall by using a foot long or so piece of 1/2" thick wood (like a strip of plywood cut to 3" x 12") putting it on the far side of the panel as you clamp with the GG.  That way the wood will absorb the torque pressure and distribute it more evenly along the drywall making it less likely to snap at the pressure point.