I think you can get by with a range of balance from centered between binding toe and heel, to the center of your binding toe piece. Once you are ahead of the binding toe piece, you are out of balance (also assuming frame of reference changes based on angle right?). Reason for this is binding toe and heel are where your boots act on the skis. Might be a little more complicated with a race plate or system binding. So you can technically balance entirely on the binding toe piece and be perfectly in balance (not creating a torque on the ski?) (Also ignoring camber at the moment because this stuff is complicated, maybe it isn't insignificant for balance so then we bring it back in). Then we would agree that you generally probably want your CoM somewhere between center of binding and binding toe piece.
Whoah. Just checked this thread. That's some detailed thinking you are doing while stuck indoors. I don't think this line of thought is going to do you any good when you get out on snow. When you are in motion on the snow you need to be thinking of how your skis interact with the snow, not where your body weight is relative to binding parts.
You need to be sensing how your outside ski's shovel and tail are interacting with the snow, and to what extent those interactions match. Are they (shovel and tail) each gripping more or less equally? Are they slipping more or less equally? If the tail is producing all the perceptible sensations between ski and snow, then you are probably back seat with the shovels light. If you can feel the front of the ski gripping the snow and the tail losing its grip and slipping away, then you are too far forward at that moment in the turn. If you can feel the tip and the tail gripping the snow the way you want them to through the entire turn, you are in control and neither too far fore or aft. This goes for slipping turns, and for hybrids (grip with slip).
Anatomy, delta, ramp angle and binding placement have impacts on how a skier accomplishes this control of tip to tail ski-snow interaction. So "it depends" makes the most sense when different skiers give advice on how to maintain this control.
Here's a list of what I've read here so far in this thread, plus some more. Personal anatomy and gear details impact what combination of these will work for you. Trial and error are called for.
Dorsiflex
--Use muscle contraction of the TA to maintain firm shin-tongue contact. Shin should rise up from the ski tilted forward diagonally, not at a right angle.
Pull feet back
--This feels as if you are trying to raise the tails behind you. Keep feet back there. Check as you ski - are feet back? (Do not pull the legs back.)
Keep hips forward
--Keep hips hovering over the fronts of the skis so that the upper body's weight hovers over the shovels. Since the tibia is pressed onto the tongue due to dorsiflexion, the forward body weight levers the shovel downward. Do not ski in the toilet seat position.
Balance over the arch
--feel your underfoot pressure focused there, not on the balls of your feet and not on your heels.
OR
Balance directly beneath the tibia
--This spot is at the back-of-arch/front-of-heel (aka "arch-heel"). Feel underfoot pressure focused on the arch-heel. This is not back-seat because the tongue-shin pressure and management of upper body position will press the shovels down.
Keep hands and arms forward
--Hold elbows in front of jacket's side seams with hands out. Arms have weight. Do not swing the arms, swing the basket of the pole. Do this from the wrist, do not swing the arrm/hand from the shoulder.
Here's my suggestion, which is what works for me dependent on my gear and anatomy. YMMV.
--In order to control shovel/tip pressure, lever the front of the ski down onto the snow. Get the levering effect by maintaining continuous tongue-shin contact and at the same time manipulating upper body forward position (move hips more forward aaaor less so). Holding/pulling feet back, maintaining dorsiflexion and keeping arms/hands forward is necessary to do this.
--In order to control tail pressure, keep body weight over the arch-heel spot. This works best when you maintain dorsiflexion and foot pull-back while managing how far forward and up your hips are.
--Manage the balance between shovel/tip pressure and tail pressure by moving the upper body either more forward or less forward as it hovers over the fronts of the skis. Arch-heel will take care of the tail pressure.
