Not quite swvalcon -- the old Rambler bodies have rails much like frame rails that run the entire length of the car. Only the newer models (63+ for Ramblers, except the 63 American, which was old style) from the early to mid 60s are built in the "three box" method (engine box, passenger box. trunk box) with the rockers being the main support for the passenger (center) box. I tink Mercededs may have been the first to make unit body cars using the three box method, not sure. I don't think AMC was the first US maker to do it, but they were the first to make "unisides". The door frame sides are all one welded piece. There is a large stamping, but a lot of reinforcement is welded in. Then the whole side unit is stood up on the edge of the floor/platform and welded on. Almost all of them are made that way now.
Just cut the floors out in sections. The rear floors aren't real bad. If you're building this as primarily a driver/cruiser you can use some type of rust neutralizing treatment or paint then put a piece of metal over the center of the rear floor (where it's rusted away) then fiberglass over the whole thing. As long as the rusted metal is sealed away from moisture and air it won't rust any more (rust is oxidation -- no oxygen, no more rust). Fiberglass on top to bond it all together and seal, rubberized undercoating underneath. But of course since you have the tools and skills simply cut one floor out at a time.
The rails pass under the front floors at an angle. Easy to see once you're underneath. There are also cross supports under the front seats. As already suggested, cut around those then clean and weld new material to the supports. As long as the main "frame" rails are reasonably solid you're good to go. those old Rambler bodies are a lot stiffer than the newer unit bodies.