After working my way through rear-end repairs on our '69, those modifications make me cringe. I'm not sure about '66, but in '69 and later years, there is something called a rear hold-down (those double rows of rivets you mentioned). It is a bent metal plate that attaches the shell to the frame and sandwiches the subfloor between the two. Without that plate, there isn't much holding the shell to the frame. However, if the trailer was gutted and only used to haul around some toys, maybe it wasn't subjected to as many stresses as a fully outfitted RV?
I've documented much of my work on ours on instagram (@lady.clementine). if you search for "rear hold down" (or some form thereof) on these forums, you should get an idea of how it goes together. Again, my knowledge is limited to '69, but you may also be missing some frame members that come down from above and give structure to that whole back section. I wouldn't expect the inner/outer skins to span such a wide area without some framing in there.
Good Luck!
-Matt
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