Where are you in Ohio?
I've seen a lot worse hang-ups than that. If I were cutting that tree down I may do it a bit differently, but here is a safer way.
As the tree now resides, most people would want to make a cut either on the top or bottom of the leaning portion of the trunk. By top I mean the portion of the trunk (above the split out) that is facing the sky. The bottom is facing the ground, and if it would have not hung up, would already be on the ground.
there is plenty of wood still attached near the trunk, and the way it is hung up looks like it is well supported and fairly stable. I would get a good long rope, chain, long tow strap, and tie it to the tree about 6 feet above the split out. I would get out the step ladder and prepare to make 2 cuts perpendicular to the top/bottom of the trunk, but not to the top or the bottom. Think of it as a compass. Top is north, bottom is south, Make you cuts on the East and West sides of the tree. When you do this, do it in this fashion. Have another person on the rope. When making the first cut, if you decide to make it on the East side, have that person with the rope on the west side of the tree. Make your cut just over half way through the trunk, then stop. Move the ladder to the other side of the tree and have the person throw the rope over to the other side of the tree you just cut on. Have them hold the rope and snug up tension on the rope. Do not have them pulling on it, just keep constant tension on it. I would make the next cut about 3-4 inches above the cut on the other side, and take that cut to about half way through. Let the saw do the cutting on its own, i.e. dont force the saw to much into the wood, constant pressure by the operator is enough to feed the saw wood. If the saw pinches, do not panic, and do not have the person pull on the rope. If you are worried about your saw, tie a rope to the tree below your cuts, leave some slack then attach to your saw. When the tree falls the rope will prevent the saw from hitting the ground. Get off you ladder, with or without the saw, then go help the person snap that little bit of tree that is still connected.
If there was a problem that pops up when you are cutting, then that is why there is a guy on the rope while you are cutting. It the tree begins to go, he should be ready with a burst of energy to pull the butt end of the cut towards him (with a safe distance between them) and away from you.
Took me longer to explain how to do it than it would to do it.