I am assuming that since the O/P says there is rot in the floor and joists, that it really isn't safe to walk into, or at least walk into and start taking panels off, in fear of the shed coming down on his head.
I like the idea of the cables, but wanted to add one small thing.
Take a look at the design of the shed, and loop the end of the cable around a whole wall in a manner that it will either pull the whole shed down at one time or will cause a single 2x4 wall stud to break, and tear towards the next one in a row. (basically a large loop in-compassing a whole wall). So I guess you will need to drill a hole at the end of a wall and loop a cable around the wall and back to the opening at the far end. Use good connectors to hold the cable loop. Now, start on the side that you want the shed to fall towards, and route the cable away from you, around the back corner and then over to the tree that you are using as a anchor. Basically if the 2x4's start ripping out, it will happen at the corner nearest your tree, but if the wall stands up to the tearing effect of the cable, the the cable being run around the back side of the shed will help to pull it over. If you start pulling and the shed just twists or spins then it was a lot stronger than you thought, and at which point, unhook the cable from the tractor and run it through the loop where it went outside the wall. That will make a choker out of it and when you pull it should collapse the walls inward. However with the collapse method you won't be able to control the direction of fall.
David from jax