Asking for advice from experienced cutters to drop a leaning tree

[Badtrees]

Hey all,
I have a dying digger pine tree leaning over my chicken coop. Normally with a leaner, I would research some techniques and experiment on my own where it doesn’t matter how they fall, (with mixed results) but in this case, the tree is leaning directly at my chicken coop and I would prefer to not make a mistake. I included a Level in the pictures to show the amount of lean because the Hillside gives it a deceptive appearance. I have a drop window of 45 to 90° of the lean without hitting the coop or other trees. I am able to pull behind me in the pictures with a cable & truck, which I planned on also employing, but I am concerned with the amount of lean that doing a standard notch cut the tree may twist and break loose of the hinge falling toward the coop, also complicating this a bit more, you can see in the first picture that It has a split trunk at the top third of the tree with a secondary trunk leaning off backward and slightly side of the lean, which is going to add some weight in what I believe to be a bad direction. I estimate this tree between 40 and 50 foot tall, roughly 20” diameter at the base. I was considering trying a tongue and groove cut on this, but I’m unsure if it would handle the side weight.

 

[Maintenance supervisor]

Tongue and groove cut is a show off cut for yard arborist when the tree is a top less post, absolutely will break sideways with any weight. The internet is full of misleading garbage.
A good open face hing is a standard cut to keep the tree on the stump till it's on the ground. Have a quality 5/8ths -3/4" rope is a guarantee to get the tree in the direction you desire. Using a pulley inconjunction with your pulling rig would be ideal.
20" DBH is standard 2" of hinge, I'd shoot for 3 and pull it over with the rope.
Trust me when I say don't cheap out on rope ,unless the coop didn't cost you any money. 15,000 lb working range should be a minimum.