Madhatte: Thanks for all the time you took with this. I'm forced to admit what you are saying is a little over my head. From a thinking/planning standpoint, how would you have approached this tree to get it to do what you want, safely, and not by accident?
Well, first, "steep and deep" is a time-honored method that certain parties hereabouts heartily recommend (hat tip to RandyMac). TOO steep is sort of a GOL thing and too deep is an easy way to lose a tree early. The trick is to get the face right. It's better to go too shallow, and fix it, than too deep, and live with it. Pretty much everybody has adjusted a face or two to make things work. Sure, sometimes you'll get it right the first time, but having the mental flexibility to work with what you have is pretty important. A very good habit to get into is to slap a wedge in the backcut as soon as there's room behind the bar. This gives you some assurance that the tree can't set back on your bar, and also gives you a place to apply force to use leverage. I try to do this even if I don't intend to pound the wedge. It just gives me more options, plus, if the wedge falls out, I know the tree is tipping, even if I happen to be looking somewhere else at the moment. SO: for this tree, a good plan would have been to make a face cut deep enough that it would take little force to wedge the top past the center of gravity, but shallow enough to allow wedging between the bar and the hingewood. With 8" wedges, 35-40% would have been OK, I think.
The comments above about using a plumb to gauge the lean are spot-on -- that tree was much better balanced than the butt alone let on. Sometimes it helps to look at it from several angles and come up with several plans so that you can reject the ones that don't work. If you only have one plan, and it fails, well, that's just a failure. More options are always good. Since you were mostly concerned with avoiding the fenceline, there were probably several other lays that would have also achieved that goal. Think them all through, as a mental exercise, to make sure the one you're going to follow is the best one. I often change my plan based on seeing something I didn't expect which I never would have seen had I not taken the time to look.
Another thing to consider, which I haven't seen mentioned yet, is assessing the soundness of the tree. It was beetle-killed, yes? You'll want to have a look at it for compromised structure, then. Look for conks up the length of the bole -- they will certainly indicate rot of some kind. Tap it around the base with a hammer or the poll of an axe. Listen for the sound to change when you strike the wood. If there are spots where it sounds different, it's likely that the wood there IS different. Duller sounds often indicate rot, while more musical tones can indicate sap accumulation, which suggests healed scarring or other structural irregularities. A sound, uniform tree should make about the same noise pretty much wherever you tap it. It's often to your benefit to pull the face from identified rotten places and to use the sounder wood for holding. This, too, could change your plan. Remember that the strongest wood is usually near the outside of the log cylinder -- the sapwood -- and can be expected to break last. If you are worried about barber-chair, it's often to your advantage to nip the corners of the hingewood for that reason -- if the most likely wood to hold on isn't there to slab, slabbing won't occur.