Thanks for all the questions, and thanks to SS for his perspective and helpful advice. I’m going to try and answer all the questions above in sequence, but please bear in mind that this is what I find useful... not sure if any of this will work for you?

1. How do I manage fine tuning focus, switching on/off stabilization or zooming; do I possess a third hand?
I wish I did; would come in useful for many more activities than just photography. As I have just the standard pair, I fine tune in the British 2-Point Sling stance using my second or third finger of my right hand. I’m blessed with long fingers, and I rarely shoot fully manual except for when I’m stalking / staked out on a shoot. The canon lenses I shoot with have the focus ring in range of those fingers (I wouldn’t buy a lens that didn’t allow that, unless I was pretty sure I would never need manual focus for that application). I practice with both fingers because I find that in cold conditions I lose sensitivity in the finger tips quickly; I use a fold-over fingerless neoprene ice fishing glove on that hand and swap fingers & covers every few minutes to prevent frostbite. 😉
I don’t switch off stabilization at all, as I’m free shooting throughout Winter (explained in my OP). When moving and stalking targets of opportunity, I prezoom before I start each stalk. Same behavior as all Special Forces Operatives around the World, and Big Game Hunters, too. You “set your sights” for maximum range you expect the engagement... and prepare to take a “very full sight” when something happens right in front of you. 😎

2. How do I manual focus tweek?)
As mentioned above, I only use one of those two fingers for manual focus tweaking when I’m in a long stance or staked out. If I’m slung and gripped for quick action... well, that’s why I buy good glass and rely on autofocus. When speed acquiring the target in Winter is key, I personally don’t have time to manually control focus as well. I’m in awe of those guru’s who can pull that trick off; I’m happy to settle for an auto-focused image somewhere near the middle of my photograph.

3. Looks like the second picture of the horse auto-focused on the scrolled woodwork behind the horse, instead of the horse itself.
Well, that’s why I supplied the download version of that pic. At a shutter speed of 0.4, aperture of f/16, and ISO of 12800, I can’t stop the immutable laws of physics and optics from working in my house, when I’m shooting in Av Mode with a 400mm lens some 15 feet from a 3 inch high target in poor light. The Photography Triangle has had its wicked way with this pic; DOF at those settings extends well past the 4 inches between the nose of the horse and the picture frame.

4. So why don't we have our cameras with long lenses (like a large rifle scope) mounted on short rifle stocks with a cable-release or blue-tooth shutter release button where the trigger would be? Then the butt of the gun stock against the shoulder and the strap on the gun stock around the back of the arm would help stabilize it all while taking the picture.
I think you can buy cheap versions of that idea, but I’ve heard they don’t work well. I’d be tempted to have one built out of a rifle stock, with a place to hold my iPhone so I can wirelessly trigger my 5D Mkiv, but I’d want to check with my local Police first... wouldn’t want them called out on SWOT duty, every time I go out on a Winter shoot. 😱

5. Or maybe just a strap from the top/bottom of the front handgrip, going under that arm, up around the back & over the shoulder to the opposite top corner of the camera would provide extra tension to stabilize it even more.
Why not try that out? For me right now, I believe I’ve managed enough stability for my shivery self when the windchill gets below -10 F, but I’ll be delighted if others take this very basic idea further? Key is getting a good sling stance, then the push - pull effect of the sling and grip will be comfortable for you. Only you can decide what’s comfortable and helps with fast shots or long waits with long lenses, in cold or windy weather and away from your tripod.

6. Now, I'm seeing that the single strap attached to the two top corners of my camera, allows the body of the camera to push forward, raising the lens, whenever tension is applied to the strap. Maybe the strap should have one side attached to the bottom of the camera, and the other side attached to the top of the camera? That should balance the tension.
I think that idea may well work for some, and would be easy to adapt. I may try that in the future. My immediate next priority is getting some sort of heat-retaining covers for my camera bodies and longer lenses.

7. Also, why not an extension plate attached to the lens tripod foot, so the short grip can be mounted more forward, nearer the front of the lens? This would lighten the weight on the front grip assuming the rear weight would be taken up by the shoulder strap.
A good question, and why my first pic shows that short rail. I could just as easily have used a longer rail, and locked the grip as far forward as I could comfortably reach with my sling stance. I suggest it all comes down to personal preference and feel, together with the type of active / passive / stalking / stakeout Winter shooting you are Planning?

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Pardon me...

Are you addressing the "Remington Support System" that I made and posted here? Or someone else?

As you are new - It is common that one makes use of the "Quote" checkbox when replying to another post.

However --

This works well, for me that is. Some might find it a bit cumbersome in that it is a bit "top-heavy". I wrap the strap around my left arm, as one would do with supporting a rifle - to hold it tight. My left had is NOT on the stock, but on the barrel of the lens (Tamron 150-600). The "trigger" is a wire remote shutter cable that I have fastened to the trigger area of the rifle stock and plugged into the Canon 5D Mark II the usual way.

This configuration allows me to freely move with the distant subject in motion and or flight. And -- Yes I do have the stabilization ON when I use this.

Not all people would find this suitable to their needs. It is good to experiment with different systems to see what works good and comfortable for each and every person.

-0-

I find that the center of gravity and the ergonomic design of the camera or rig (camera. long lens, flash bracket etc.) have more to do with its ease of handling and maintaining steadiness than their actual weight or length. I have used relatively heavy cameras and rigs that were easier and more comfortable to use and hold steady than cameras lenses and accessory combination that were lighter but tended to be more unwieldy because of their shape, industrial design, location of their controls or intrinsic center of gravity.

As an example- In my medium format gear, My Hasselblad with a given lens is the same weight as My Mamiya
RZ 67 but I find the Hasselblad much easier to manage in hand-held situations.

It's a fact, however, that some cameras, lenses and rigs are so heavy that the do require more physical strength in the photographer's upper body, arms and hands in order to maintain safe and steady operation. Many years ago, I did quite a bit of work with a handheld 4x5 Linhoff press camera- I started to develop forearms like "Popeye the Sailor"! The camera, Graphmatic film holder, bracket and flash head weighed in at 13 lbs., however, with their very well designed hand grip, the entire rig was surprisingly easy to steady.

Point is, if someone needs to use and hand-hold an ensemble of heavy gear such as a larger camera, a camera with a long and heavy lens, a larger flash unit on a bracket or a compendium lens shade, they should create a support system to accommodate it by shifting the center of gravity and enabling ergonomic handling. There are grips, shoulder harnesses, gun-stock mounts, belt pods, special camera straps and of course, mono-pods. Sometimes we just have to improvise something using some of the aforementioned accessories.
If you can somehow establish a better center of gravity you can ofttimes solve weight or bulk issues.

There are, of many specialized car and truck window mounts, gyroscopic camera mounts for aerial photography, gimbels and it seems that new support gear is being introduced all the time. Some of this gear is expensive but pays off if you do a substantial amount of work that requires special camera stabilization gear.

There are also causes of unwanted camera shake and movement such as mirror slap, and poor shutter release technique, especially if the shutter release is in an awkward location. Sometimes just using a cable release or electronic release that is wired or mechanically integrated into the grip will help to maintain steadiness and minimize shake. If the release is badly located or hard to actuate, folks ted to poke at it rater than exerting soft even pressure.

Another trick- Many years ago, a friend of mine who is a cinematographer showed me something that he does to cope with very heavy motion picture cameras when they have to be hand held. He sets up the camera and grips as I have explained but the "rehearses" various movements sometimes in front of a mirror. I am talking about holding the camera in place with his eye to the viewfinder and then kneeling, rising, changing heights, panning, "dolly" shots, following, tilting upward and downward etc. - basically simulations of shots that would normally be done on a tripod, a dolly, or with the camera mounted on tracks or nowadays with a "Steadicam". I adopted this method and modified it to make sure I could handle my rig from all the require positions without shake or yanking the camera out of level or composition while attempting to balance or compensate for the wight or imbalance. This was especially handy when designing a set up with heavy gear.

My advice is to assemble a system that will establish a balanced center of gravity and test it out on a dry run before you take it out on an important shoot or event. Try the "practice in the mirror method" that I have alluded to and check out the results with you images at a high degree of enlargement. As others have suggested, sometimes all that is needed is a simple inexpensive grip or bracket, wooden handle with with a strong well anchored screw to match your tripod socket on the camera or lens collar. The only word of caution is to make certain that whatever you rig up is strong and safe and will not result in losing your grip and dropping a camera or lens or even injuring yourself.See that metal parts don't have rough edges and use felt, rubber or cork pads or gaskets to prevent marring the finishes of your gear.

Don't be afraid to improvise in a hitch. If you find yourself out somewhere and you forgot you tripod or grip, don't forget some of the old and time honored methods of steadying a camera by bracing it against a wall, a ledge, uinsg a bean bag, pillow, a folded up jacket or blanket and buffering shake and vibration by placing you elbows, and upper arm against your body holding the camerin your right hand and cradling the lens with your left hand- take a deep breath and squeeze- but don't poke the release button.