Ah, you know what they say: An Airstream is like an onion, as you peel away the layers, you just have to cry...
Many a shell off started with replacing the carpet...
Anyhow, easy question first, no, parbond and trempro are not the same thing, but they serve much the same purpose. Trempro 634 is usually refered to by its antiquated name of Vulkem. Not sure about the 644.
The body shape of your trailer has much to do with the rotted floor in the rear. Water glides down the outside of it and when it hits that lower beltline, it is practically channeled into the end-grain of the wood floor. Many restorers have addressed this condition by essentially putting an L shaped piece of flashing at the rear so that the water comes down the trailer, is directed out onto the base of the L, and then runs off into the bumper trunk.
You may have other leaks as well: every rivet and every seam could be a culprit. If you want to shotgun it, then clean every seam the best you can, and then put a bead of sealant along it. Check each rivet and see if it is loose-- a loose rivet will leak quite handily. The plumbing stacks are another obvious culprit. If they are still designed like they were in the 70's, with the rubber gasket between the metal and the pipe, then that gasket is probably completely shot and funneling water right into your trailer.
Some windows also tend to catch water in the frame, and eventually it either overflows, or leaks through a pop rivet hole into the interior.