I feel you are making it more complicated than it needs to be. My opinion is with a 1" hinge you'd have a hard time getting that on the ground with a wedge and rope alone (without a vehicle) if the wood is sound. There is very little to no risk for barber chair as the trunk is unloaded. It appears to have some rot so that lowers the chance of a chair. A deep open face notch with a 1" hinge will be plenty to control it to the ground. Just a normal back cut is all it needs. Back away as it starts to go over.Just went out and measured the height - it's actually 13' tall. And the angle of lean is probably more like 20 degrees. The tree is not on my property, and I hadn't seen it in a couple of days, so I forgot how pronounced the lean was.
Below are some photos so you can see better what I've got. I'm thinking I will take BC's advice with a bigger, deeper notch and narrower hinge - maybe 1-1/2" or 2" as a compromise; a one inch doesn't seem like enough of a hinge to me to control the fall well. I'm also leaning toward using a plunge cut from both sides from the back of the hinge to a point that will leave a strap about 3" or 4" thick at the back of the tree. Then finish by cutting off the strap from the back, move away and have my friend start pulling it down with the pickup if it doesn't fall by itself. However given the amount of lean I think it just may fall by itself without any help as long as I don't leave the hinge too thick.
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Ever try to break a 1" thick by 4" wide green pine board by hand?