Just build the wall behind the cooking line per the ‘NON-combustible’ details.  Use mineral wool insulation between the ‘metal’ studs; add ‘metal’ stiffeners horizontally, if needed, flush with the studs or as a spacer to flush the SS sheet to the finished wall.  … Then the required Clearance would be ‘0’.   

So no wood behind hot equip. then?

 
That is what the Minnesota HD guide detail states above and the detail is the same for many other State HDs & Codes.   The problem is not hard or costly the solve.