Jayco bed causing rear wall to bow out

Jayco bult the back wall of the 28 FKS a little oddly, with the hinged bed having no other support than the back wall. I noticed last year that my back wall was bowed out, and that it had pulled away from the bed stands.

Pics - (link to pictures)

I'm thinking about doing the repair myself. I want to replace the little 2x2 hinge mount with a 2x4 that runs the entire length of the back wall, and giving it some extra support down to the floor. It would probably be beneficial to build a better box under the bed stands, to add to the support and stability.