You will find that the thicker the wall tubing is the more easily the tubing is to bend with out wrinkling. You will have to do a trial and error attempt with some tubing samples. You may find that 1 5/8" .083 is hard to get a good 90 deg bend on but if you use the next thicker wall thickness it bends perfect. This is common and there is not a down side but the extra weight to using thicker wall tubing. SFI is minimum specs.
The body. The reason I would remove the doors is only to relieve the A pilar while you are removing every thing that it is hooked to that supports it. The extra weight of the door will just tax your back and the car form while sitting on saw horses in the corner. The braces I was refering to were to create a cradel that your body can sit on supporting it adequetly to prevent damage to the rockers if that applies. I have never built a Cuda before and do not have a visual in mind on your car chassis. The body needs the front fenders removed and the doors to lighten the body so you can pick up the body and do occasional clearence checks along the way. The body will be like an empty refridgerator box when the floor is cut out. You need to know what the original dimensions are between rockers and respect the original blueprint of width dimensions you establish and set it exactly over the center or the chassis in mock up.
Welding is required to the roof near the A and B pillar's to the cage so the paint is gona get damaged to an extent. The cage and the body will become one when you are done so you need to support the body every where you can easily to hold the body in its exact original form that you are going to re animate when you hang it on the chassis. Put the doors back in the jamb to fit the openings perfect when you are done picking it up over the chassis.
I don't want your head to explode, but there are quite a few steps required to build a car from scratch. As long as you understand everything about drive line angles, the geometry built in to in the front end mounting locations, and have a basic understanding or roll centers, torque vectors and enjoy physics. Everything is real simple to do it is just making the first choice which dictates the next choice and so on.
I had this boss that used to say (if it were easy every body would be doing it bud) and somehow that was supposed to make me feel better.
It is easy to build a car but it does require a lot of choices that dictate other choices. But then again it can be very rewarding to build your own car if you are willing to do it until you are done.
Bruce