I was facing similar issues when I started building my TVR.....the factory frame was 1.5"/.080 round and square tubing. It is primarily a tubular backbone chassis with small outriggers to catch/support the body. I acthally think that the fiberglass body might have been counted on somewhat to add some rigidity. The frame weighed maybe 200 pounds, tops.
If you are building off of the existing chassis, I would look into trying to include some sort of tubular outriggers. In your first pic, something like those lower black tubes that run out from the center spine and between the wheels. Instead of the small round tubing, go with something like 2x3 or 2x4 rectangular tubing. Triangulate the rectangular space that this creates and you should improve the torsional rigidity tremendously. This new structure will also give you a place to run the rollbar/cage members to.
For the rear-going legs of the bar/cage I would look into running a piece of square tubing between the chassis shock towers, then run the rear legs to it in an "X" instead of just going straight back.
Good luck! As I'm learning with my project, fabrication seems to be more about the thought and planning that goes into it than the actual work. I seem to spend more time at the shop talking about the project with the guy doing the work than I think he actually spends doing the bending/cutting/etc.
Too bad you aren't closer to DFW -- can't recommend the guy doing my stuff high enough. Very good attention to detail, good prices!
-jeff d