You still dont seem to undestand either of my comments. The danger related to the barber chair is not about the direction of fall. The danger is a tree like you describe can slab (split) without a front notch, actually it can split even with a front notch with the heavy lean like your tree had. The split does not happen when the tree is falling but when you are still making your felling notch. Many year ago I was felling large sticks on a logging show where a faller was killed like this. I had a large oak split like this even with a front notch. The back half of the trunk split from the felling notch up about 25'. The split back slab kicked back straight behind the tree. I was standing to the side of the tree as I always do for this very reason. It happened in a heart beat. It just missed taking my head off. I had my old 075 stihl saw and moved very fast to escape to the side I was standing on, with saw in hand of course. But, it was still a 50/50 chance that the tree which now was falling without any control would kill me. There was no lesson for me to learn from this as I had done everything text book. ALWAYS put a front notch.
Second issue, the hard hat. Heavy lean and direction of fall have very little to do with this danger. Besides, the hard hat wont help you if the tree falls on you. The hard hat protects from widow makers- branches that fall on you as the tree is on its way to earth. You are thinking that this danger is from the branches of the tree you felled. That is a danger. But the bigger danger is from your tree knocking a branch off a standing tree in front of your tree as it falls. It can fling that branch in your direction no matter your escape route. On another text book example I was well away, the stick was almost on the ground, I saw or heard nothing. I was hit on top of the hard hat with such a branch. Knocked out and had to take the rest of the day off, but lived.