When I was just a young pup, I had an ash tree barber chair on me, it could have taken my head off. A quick lesson, it was. I have never had one do it since. You had too much hinge left
Plunge cutting as Jim described works well, plunging the saw takes some practice and something I am not going to go into, find someone local to show you how it is done. I would even venture a video wouldn't do it justice. It is safe and allows you to insert wedges to keep the tree from pinching the bar, or back the skidder up to, and give the tree to give it a push, while you still have two points attached.
I would encourage you to keep at it and mix the species too. I know the feeling, I have shot a number of animals hunting and trapping. The hardest time I had to pull the trigger was on a goat we had, the first one we had for slaughter. Trees are not much different.
Paul, it is not all just drawing pictures and calculating, you have started from scratch, it isn't a cake mix where you just add an egg. Adding the egg does take you into the other forum Mo mentioned, studies have been done.
Tim
