At 3/16 thick by 96 inch gap I'm getting more than 3/8 inch deflection in the center from a 3/16 plate suspended across a gap that far by the edges from gravity alone. In my mockup, I can't even get it to suspend unless I clamp both edges securely down and put the plate in active tension. Welding at the corners? Not along all sides?
That small a frame is not sufficient to hold the "drumhead" tension needed.