If you end up using the tractor and FEL method, I would lower the bucket until it almost touched the tree then chain it up. You don't want to have to lift the bucket any higher than necessary.
I agree that a pickup might pull it out, and if that's all I had I would probably try it myself, but this is a job tailor made for a tractor. Just above idle, and let the torque and gearing work for you....slowly, and controllably.
