Great discussion!
My rules of thumb are similar. But mainly i watch 2 things specifically to determine exactly how hard to apply these standards.
1) is to undermine beyond the Center of Gravity well enough to a)want to fall in chosen direction + b)flex the fiber of hinge to do so Also ***** how high CG is from proposed hinge pivot height.
2)Bring the back of the back of the hinge to the approximate widest part of the tree; especially on the control/anti-lean side for best leverage against sidelean or side pushes during fall (from other obstacles in path).
No. 1 is generally preset for you; lean away from hinge; hopefully fairly in falling direction. But covers the short/stubby extreme example by SmokeChaser too. If you can't bring the hinge pivot back far enough to accomplish this; you must either push or pull.
No. 2 Takes into consideration sidelean control needs and non-perfectly round stumps, rotted areas etc. i always face tree; then inspect face for decay and dryness. Decay is bad/bad. Dry/dead/ frozen wood can still push; but is less helpful for tension/pull; being less elastic. Both push and pull is needed in hinge/face machine. So i assess where tension and compression wood is needed; and if the face shows that type of condition possible in those specific positions. And dead and decayed are 2 different categories.
i believe in push (mostly by wedge) and pull (mostly by rope) to force a stronger hinge; just relieve these added forces when tree starts to move. Forces at FirstFolding(i define this time period as done when the tree will travel on it's own) determine hinge strength; more force forces hinge stronger. Hinge strength just being a reflection of the forces on it at this point in time; so we 'fake it out', to 'think' it has a bigger tree to steer! Additional forces after FirstFolding tax the previously set strength of the hinge; so essentially weaken it; so we relieve them. This is one thing a wedge works for us automatically; when the tree lifts, the wedge stops pushing.
i think the slanted BackCut is a no-no; in that the 'back stop' is weaker in case of sit back. If the tree sits back against a slanted back stop; the immense leveraged force goes more across the column of the stump/ rather than served down into the strength of the column. Also, there is weaker backstop to push off with wedge if needed for the same reason; and the wedge is pushing more straight ahead to bring tree straight ahead. But in a straight backcut with wedge pounded in, the wedge lifts, to serve forward. So the former is more of a linear applied force, whereby the latter is more leveraged arc; taking a longer route to achieve same result/direction factor. Another consideration in wedging is that the farther back the hinge; the less leveraged distance wedge has from it's lift position to the pivot of the hinge.
i might have slanted the backcut on one of them trees; to not cut into another tree behind it. and still have hinge leverage/height where i wanted; if it was safer like that.
In good wood/up to the task, i prefer to let the hinge steer mostly; and apply all additional / hinge strength increasing forces(rope and wedge) to the gunned face/ center. If pulling with line or pushing with wedge to steer; then we are unloading the hinge from it's task some. i'd rather force the hinge stronger, then taper the hinge to steer; so that my exerted additional forces go through another multiplier (hinge); instead of unloading hinge from imbalance, and replacing it with my effort; allow the mechanics to work for you.
Works great in-tree too; especially if you kerf dutch the sidelean or push from side(not full face) to work in concert with the extra pull of tapered hinge. Then, we have a pull and push in same direction and rotational, with counter pull/pushes dropped out of the equation (when kerf closes and tapered doesn't).