Bartamos, I still disagree. Feel free to find one of the original engineers and prove me wrong, and I'll eat crow if you do. The frame wasn't "designed" to flex, it just did. At that point in time chassis design was not highly sophisticated and economics as always dictated a simple approach to manufacturing using simple materials. The body is not nearly so rigid as you imply but more importantly the points where the body attaches to the frame are not "hard points" intended to tie the two structures together. Rather, they are there to literally keep the body from falling off the frame. Think of all the pictures of guys driving around on their bolt with nothing more than the frame, engine and a lawn chair.
I'd agree with your suggestion to have the welding done by a pro, good advice in that application. If the goal is to reduce flex, adding an L shape will do little to reduce it, stick with something that turns an open cross section into a closed one (think tubular). I'd also lean towards welding the shapes on rather than bolting. Bolted joints are horribly inefficient compared to a weld when it comes to load transfer.
