The whole point of the "pull back" is to adjust the position of your CoM so that you aren't in the back seat as you proceed down the back of the mogul. Think about the ramp as you exit a chairlift. When you get off a chairlift, you stand up, lean forward a bit, and glide down. Imagine now that for whatever reason, your weight is back as you start down that ramp. Its like slipping on a banana peel. You see it with beginners exiting chair lifts all the time, but they are leaning back out of fear. With moguls its a similar scenario. You are at the top of a ramp (back of the mogul), but in this case, your last movement as you came into the bump with your feet forward, has left your CoM behind your feet. So without a correction, your are heading down that ramp in the back seat. The correction you need is the "pull back".
Folding over at the waist isn't really considered a good thing. What you see in the images you provided isn't folding over at the waist so much as it is part of the knees coming up. The motion is happening at the hip joints. The skiers back should remain more or less straight. There shouldn't be much bending at the waist. That doesn't mean it doesn't happen, but the goal is to minimize it. With good mogul skiing technique, the upper body should be very quiet. You should be able to balance a glass of water on top of your head and not spill a drop. All of the work is being done from the hip sockets down. If you are absorbing properly, there shouldn't be a big slam to throw your shoulders forward and cause you to bend at the waist. That being said, even really good bump skiers will sometimes experience a little bit of a slam that throws their shoulders forward, and chances are they can't keep a glass of water on top of their head without spilling it, but these are the things they are striving for.
When you say you are never pulling your feet back, can you elaborate a little bit on what you mean. Part of my issue with the term "pulling back" is that to me it doesn't make sense as a pulling motion. Could it be that your interpretation of what you actually do is different even though you are doing the same movement (or at least same type of movement). Do you do anything to correct for your weight being a little bit back before heading down the back of a mogul? Your approach to moguls is a little bit different from what is what I would call "textbook mogul technique" (if there is such a thing). From the little I have seen, you ride up, take a little bit of air, and land somewhere on the back, but not really in the trough. You ski the bump rather than the troughs between them. When you land on the back, where is your CoM? If its back, chances are those landings will be a bit scary. If its centered or forward, how did it get there? Your last contact with the ground was as you rode up the front of the bump. Somewhere right before your feet left the ground, there has to be a correction to bring your CoM from behind your feet to ahead of your feet. That correction would be essentially the same as "pulling back". Just like taking air off a kicker, when you are about to leave the ground, you push your hips forward to transfer the CoM forward. If you didn't, your vertical axis wouldn't start to rotate down the hill so that your feet will match the slope of your landing. Its all the same concept as "pulling back". It is simply a CoM correction intended to accommodate a change from an uphill slope to a downhill slope without finding yourself in the back seat.
With regard to what I said earlier about maintaining snow contact, this is another one of those aspects of "textbook" skiing that often isn't achieved. For me, its a priority in the bumps, but for a lot of really good bump skiers, they don't mind if their feet come off the ground. Its another goal to strive for. Look back at the picture of Hannah Kearney I posted, and look at what her comment was. She holds a Gold and a Bronze medal in Women's Olympic Moguls, and is quite possibly the best female mogul skier in the world, and I might even go as far as to say ever (I'm a big Hannah fan), but she even on occasion lets her feet come off the ground. But she also pointed out that she should work on it, which suggests to me that she considers snow contact to be the correct way to do it. This doesn't mean that you should abandon your approach to mogul skiing, but you should understand that your approach isn't exactly going to match the "textbook" approach, and applying techniques like "pulling back" might be a little bit tricky because its usually explained in the context of "textbook" skiing. As for not skiing in the rut, and avoiding the icy back side of the mogul, there is nothing wrong with that, but again, "textbook" mogul skiing usually refers to taking a zipper line through the troughs. The principles are still the same though. Lets not make mogul skiing some mystical experience where all of a sudden the rules change. All we are doing is skiing up a bump, then down the other side. If you were skiing over a whale-back you would ride up, your weight would come forward as you roll over the top, and would continue forward down the back. Imagine that same whale-back slightly smaller, and keep shrinking it down until its the size of a typical mogul. Then line up a bunch of them and let it rip.
The part I didn't understand was where you tried to describe flexing and extension using =. Just kind of lost me, but if my description was essentially the same as yours would be, I think we are good on that point.
One thing that still sticks out to me, is the way you describe pointing your tips down the back side of the mogul. I'm not sure if you are doing anything wrong, but I can remember reading your descriptions a few times and thinking something felt off about it. When we talk about pointing our tips, its not just about your skis pointing down the back of the mogul, its about the skier attached to those skis pointing the same way. So when you point your toes down the back, you aren't just getting the tips down, you are rotating forward as a whole. If you fail to make the correction to the CoM, you can point your skis down the back, but you won't ski away from it most likely. Picture taking air off the bump, your weight slightly back because there was no correction, and you do a backscratcher. In the backscratcher, your toes will come pretty close to pointing down the back side of the bump because your weight is already tipped back. Would you want to land in this position? So instead of that catastrophe, we make a correction, which brings the CoM forward. Essentially you are rotating the whole skier around an axle directly under the feet. This is how it is possible to maintain shin pressure as you head down the backside of the bump, assuming your feet are on the snow. If its happening in the air, when your feet hit, you will fall right into a position with flexed ankles and shin pressure.