Step 3: Build a Torsion Box
Cut the plywood sheet into a 32" x 8' panel and build a support structure of 2"x4"s beneath it. The more 2"x4"s you run beneath the plywood the more rigid and stiff the torsion box will be. I didn't go too crazy and the cart is plenty strong since it's going to get a lot of additional reinforcement.
Cut large triangular plywood pieces and screw them into the four corners so that you have a surface to mount the heavy duty locking casters to when the time comes.