Stainless steel type and gauge for pizza oven
I build a lot of pizza ovens each year, steel and stainless.
I use 11 to 14 gauge(.120" to .075") in steel and always 16 gauge in stainless 304.  

Warping occurs on the front panel where is the door opening, mostly the top part, just and iron angle inside where you doubt it could warp.  If the sheet is rounded or bent, it add strength to it so it never warps at the dome.  Hope it can help.