I found a heavier gauge of wire and redesigned the hooks for the PVC so that the won't come undone. I also added another bar to the frame so the cover has more support in the middle. The difference was dramatic - putting a lot of weight on the cover will cause the grids to start bending before anything else budges. Much better.
I've posted instructions on how to make the hooks and the frames as well as assembling the cage. If you're interested, the instructions are on Outdoor Pen How-To.