A big dozer could have it on the ground in a hour by digging out around the roots.
I have a large rotten tree that snapped off about 40' up, came down and stuck in a fork, then teeter tottered heavy end down right over our walking trail about 8' off the ground. Like the suggestions here, I left it alone and waited for Mother Nature to make a move. After almost a year, we had some high winds w/T-storms last week. Walking the dogs I found that another tree, well over 100' tall had blown over at the root ball. You betcha...., it came down right over that fork and hung up on it just like the O/P's tree, forcing the teeter totter section 30' up off the ground now.......what are the odds? And what a mess!