The type of distortion you are describing can occur on large flat thin sheets (with or without flanges) when there is a localized heat source that creates an temperature hot spot and metal expansion in a localized region of the sheet's surface.
Changing the sheet material to galvanized aluminum will have no effect in reducing the warping. Also, there will be no real benefits from rolling the flange edges or flange corners.
The only effective way to minimize the warping is to minimize the the localized hot spot source component in the electrical assembly.
If possible, clamping the pan assembly corners to a more substantial base plate could reduce the the degree of overall warping of the assembly.