Let me offer a suggestion or two on this. Don't tack the plates onto the floor right away. Cut a hole in the floor under the plates, then fab the plates up but just set them in place. Build the cage with the main bars just sitting on the plates. Then when it is time to weld over the top of the hoop, you can remove the plates and drop the cage down through the floor, and get access over the top of the main hoop. This makes it a lot easier to weld, and you can get the main hoop positioned right up against the top of the headliner or roof for the final installation.
Too bad you haven't got a bender, you could put a bend in the side bars so that they clear your armrests. I do that on all my cars, and also make the side bars swing-out for easier access.
Also pay attention to the D bars; these are the short bars that come off the main hoop and angle down to the floor. NHRA used to allow those to weld onto more steel plates on the floor of the car, but they are now asking that they weld to some kind of frame member. I got stung on that one back in 2006 with my Mach 1, and had to cut the bars out and revise the installation. I add subframe connectors to my unibody cars, and cut a hole in the floor where the subframe connector runs, and weld the D bar to the subframe connector. That passes muster with my local NHRA tech guy.