per OP and post *12; It causes wonder about many materials. First thought is that 11 layer plywood I associate with European furniture, also found in boat building. Wouldn't need to be 100%, mainly outside and sliding surfaces. It could deliver added clamp pressure, which may or not be useful. Controlling that is a function of screw diameter and thread pitch.
I'd also be tempted to add a swivel jaw, per those Parker metal working vises, but tend to go unnecessarily hog wild on features.