Well, this is what i did, be it right, wrong or indifferent. I took jack stands and placed them on my work table. I laid the housing face down on the stands (one one each axle tube and then one in the opening of the housing) and used ratchet straps to secure it from the very ends so as not to burn them when welding. I then proceeded to weld the brace on using very short bursts and moving from spot to spot. I continued stitch welding it until I had it welded solid. If you spend too much time in one spot it will start making a popping sound, if/when it does move to a different area.
As you're welding it will more than likely want to pull the axle tubes back as it gets hot, that's why I did it the way I did.
I made my brace for about 5 bucks of scrap steel I picked up from a local steel shop, just cutting and fitting until I had it where I wanted it and then welded it up.
It seems to work fine, slow and easy is the recipe.
A pic of after the brace welded on and primed and another of the completed project.