When welding.........

(Responding to this while eating my luch at work as a welder/custom fabricator.) I would do 1"-2" sections staggered from side to side, let it cool down and weld the whole thing solid. That way you wont get any water trapped inbetween the brace and rear housing and start rusting from the inside out.
I would do 2 1"-2" sections at a time on each side then let it cool. It may take a wile to finish but atleast it wont warp on you.