I am only an observer, but I did alot of it while watching both the track-hoe and the D-6 in action with timber.
The prep was similar for both; cut the roots. The track-hoe takes a bucket from the left side, a bucket from the front right side, an bucket or two from the close side, then pushes about 8 - 10 feet up, monitoring the cracking sounds and bending trunk reactions to make sure she don't snap off. It wasn't unusual to grab it from the far side and give a yank to loosen, but ultimately they fell away from the equipment. Use the bucket to sweep the spoil back into the hole.
The dozer...the tilting blade is the cat sass. It made me smile watching Red run that thing. He would bang fwr/rr, left, right, snapping it around like a kid pushing a tonka dozer. He would line up to the right of the tree, tilt the blade down at the root ball, and dig in to cut the roots....way down. Go to the other side and do the same. Then, straight into the trunk and push, ease off, push...down she goes.