The factory mounts are designed to twist and/or flex? I think you're mistaken. What I think they are is as thin (cheap) as they can possibly be without failing under normal driving conditions. If you look at them you'll notice that the edges distant from the axle tube are rolled on them making them stucturally stronger than if they were flat tabs made out of the same material. The benefit is similar to using a dimple in a piece of thin gauge plate. When you see the LCA box flex, you are actually seeing the lower control arm brackets "working" on failure.
Adding a skid like plate to the bottom of them will add strength to the box itself. It will also increase the weld surface area between them and the axle housing. As far as options go, it is a distant second from repalcing them with a stucturally superior reinforced LCA box made from thicker material but boxing them will be far better than nothing.