JimmyJ the good Lord has just been watching over you if you haven't had any barber chair on you yet. The tree is tensioned the way it is now. It is hard to see from that photo if all of the tension is at the top of the tree where it is hung up forcing the tension to go in an arc under the tree. Or if the root ball is holding most of the weight and the tension is on the topside of a the tree. Plunge cutting might work to decrease the barber chair scenario. What I have done in the past is wrapped a strong cable around the base below the cut. Then taken the cable above where you are going to cut. And then used cable clamps to make a very short leash on the tree. If it tries to spring up or any direction the short leash on the cable should stop it.
Another method we use is sling shot a line over the tree as high as you can. Then pull a large rope or cable up and over. Bring the end back around to make a loop. Attach your rope or cable end to people or a tractor and see if you can pull it out of the branches. Just don't wrap the rope around your wrist if you use people to pull it.. Rope burn hurts like heck!
Looking closer at the picture it looks like it is resting on the stump maybe with a little hinge wood left. If you can get your cable up next to the break. Wrap the cable around that and pull with the tractor from a good distance. That should remove it's resting point and maybe let the butt come down. Chances are the top will still be hung.
