The picture doesn't show it well, but there is probably still 6-8 inches thick of wood that is hinged to the main tree (on the left). I don't think I'll be able to simply pull it off. I think I have to cut it.
My thought was go up a ladder on the left tree, and cut it at the hinge point, so it drops down away from the tree. I don't like the idea of being on a ladder, 15 ft in the air, when everything let's go, though. A lot can go wrong quickly, including the tree potentially springing back (and bucking me off the ladder) when the split portion is cut off.