The rules mention that method. I have it on pretty good authority that a cage like you're planning should pass tech, provided all other requirements are met. Nevertheless, check first.
The thought of sandwiching .060 steel floorboards with plates just doesn't sound too safe compared to a real cage.
I was told the idea is to build the car around the cage, rather than install the cage in the car. It's verbal semantics, but intuitively, it makes sense.