How thick is that limb holding up the leaning tree?
I just took down a leaner that was being held up by another tree near our well house. The holding limb is only 2-3 inches. The leaner was only leaning about 70 degrees. I tried to push it with the tractor and the tree did not move. The leaner was 15ish inches on the stump.
So it was going to be done the hard way. I first cleared out the area the tree would land in as well as where I would be cutting. I then hooked a comealong to the tree and put some tension on the tree. I tried to pull the leaner over enough for it to fall but the stump was not going to allow this to happen. So I cut the leaner and pulled with the comealong. That put enough weight on the holding limb which broke and the lean came on down.
Now I have a widow maker in that broken limb since its still hanging in the tree.

But it will come down in the next good wind storm.
Why did I use the comealong instead of the tractor? The leaner was just at the edge of the woods and getting the tractor in there would likely damage the roots of a large tree. I was able to place the comealong such that a decent size tree was between me and the leaning tree so it was safer. As it was, whenever I heard the leaner make some noise I ran like a scalded dog.

I could not do that on the tractor.
I have a leaner, 30+ inches, that I'm waiting for mother nature to take down. The holding tree and a couple of others died. I think lightning got them. The only way to get them down safely is with a large equipment or a cherry picker.
I watched a tree service clear a bunch of pines from our neighbor back in the city. They where impressive. And scary. No safety equipment except gloves and maybe a harness. They climbed those trees to top them out. They would attach lines to the section that was being cut so that it would drop away from a fence and the guys house. Short of this kinda of skill/daring not sure how that tree will get down without risk and/or money if the limb/tree is real big.
Later,
Dan