Steel Selection...

Let's get inventive; I think it must not be a question of type of steel, but what your construction is and how it is welded and how the in-built stresses while welding are then partially released whilst cooking. I see the problem in that you paint and at the same time cook; so I suggest: make a refractary or even gypsum mold strong enough not be moved by the adaptation whilst cooking. Then, whith your part inside, cook the contraption to if you want even higher temperature than for painting will be; then you will cool, open your relieved contraption. You then rinse, cleanse, or even grind what needed and then you paint and cook in such a way that through proper support you don't get further movement, what maybe difficult for fine finish. It seems apparent that the temperature is high enough as to release such deformations, so, use the lower the temperatures compatible with your finish painting good cure. Also, use better in the first stage a bit higher the temperature (prior to painting).