I have used foam board many times. No issues with warping. It all comes down to bracing and overall structure design. I build mine with a initial plan of how it will be constructed and use all rabbit joints and a ton of interior bracing. I also paint it with spray paint. Only one side. Very light mist coats. Seal all edges with foam paste and acrylic texture paste. I also remove sections of the paper and carve brick detail and such. I am at work now. But when I get home I will show some pictures of how I brace my structures. And provide any other details you would like to know.
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