Preventing Warping when Roasting at High Temperature
The bottom surface of the pan will expand as it heats. The edges will also expand but they won’t be able to expand as much as the bottom surface. This will cause the warping, even cracking.

As you have mentioned one way of avoiding this is having one or two edges, as the cookie sheets would have. These pans will not create such tension as the surfaces of the pans expand.

In your case however I think you need thicker pans that can withstand the tension.