I'm going to be doing a simular repair on a Caravanner (same platform as your unit). From the information I have gathered from others that have done this repair your on the right track. There are a bunch of posts worth reading in the forums that cover this.
First thing you need to understand is the body is structural and a major part of the strenght of the unit. The frame is built light as a result and that's why these units weighed so much less then anything else in it's size. As a result it ies best, whenever possible, to replace a full width section of the floor back to the factory seam. The front 4 ft and rear 4 ft can be done without removing the body. The U channels changes shape at the first rib. once you get into that part of the floor it's usualy best to remove the body.
Now that old original tile is full of aspestos. Take the proper precautions.
The trick to replacing the front and rear ir to remove the rub stip the ends at the first rib. On the inside pull the lowered inner body pannels to access the lag bolts. Now on the toung end it gets a little trick because your going to be fighting the natural ballance of the trailer. On the rear you would strap the bumper to something heavy. Once you remove the rub strip and any rivits up to the first rib you lower the jack and this will cause the trailer to open like a clam. You might ahave to loosen the U channel lag bolts further back but not need to mess with the Bucked rivets past the rub strip. You only need about 2 inches and then you can slide the deck in or out.
On the front your going to need to take the tanks and anything above the frame off and that might include the jack. You might be able to work it in there with the Jack in place. Since your fighting the natural ballance your going to have to figure out how to hold the rear of the trailer down.
When doing the rear floor I have been told it only takes about 200lb worth of weight to get it to open up. You might be able to put some jack stand under the frame a couple feet in front of the tires (put a 4x4 that's full width of the unit under the trailer to put the stands under) and get the same effect by lowering the tounge jack or a floor jack under the tounge if you take the jpole jack off.
You want to try to remove the bad floor in one peice if possible so you can use it as a templet for the new peice.
InlandRV.com and www.airstreamdreams.com
both sell Olympic rivets. These can be finished to look like the factory buck'd Rivet. The finish tool is EXPENSIVE but some people have had very good results using a concave qrinding stone on a dremel tool to finish the heads. Inland has recently put a drill bit kit together that has all the proper size drill bits for the rivets.
Good luck with it. I'm hoping to start taking our 59 apart tomorrow to start the same process.