I can't see the distortion that you are talking about (damm watermarks). What kind of distortions are these? How did you rigged the lap? Because I'm thinking... it might be that another joint (in the arm) is affecting that surface, and so when you move the first joint part of the surface moves but the other part stays because it's still obeying the second joint. That happens with smooth binding I think. Because this is not an organic model you should probably just parent each piece to a joint.