We all have different ways of doing things and in many cases different levels of equipment. If I can interject a couple of things here though that you all might find helpful.
First off, I agree the two pronged openers are the worst, but the three prong of that style are not all that much better IMO. If you are using one of these openers, the best way to use it is with a case holder, that is clamped into a bench vice. This keeps the case steady as you use an opener to loosen the case back. I would then place the opener on the case back and use the palm of one hand to hold it flat while turning it with the other. The case back in that video was certainly not very tight, so when you do get a tight one, or one that is sealed with a gooped up gasket, having the case holder and vice will be very helpful.
I would make sure there are no sharp corners on the prongs of the opener you use (remember most tools, even expensive tools, do not come ready to use and must be looked at and prepared prior to use) as this will reduce the chances of scratches when simply placing the tool in the grooves and adjusting it for size - as you can see it can be awkward to do in the video.
Often if the threads are not great the case back will be different to turn with your fingers as shown, and for this reason I always keep a case opening ball in my bench. They are cheap, effective, and can be used to loosen case backs that are not really tight, and you won't even need the Jaxa style opener. These balls are non-marking and if inflated to the proper level, and kept clean, work very well.
One thing not mentioned is to clean around the case back before opening the case. I would recommend running a sharp toothpick (the sturdy round type) around the case back to remove any dirt and debris before loosening the back - you don't want anything going into the case. A hand held air puffer works well for getting rid of this once you have loosened the dirt from the case back area, but you can also wipe it with a cloth.
Also note that when the case back is loose and can be removed, the only thing holding the movement in the case is the stem. The case screws on a Speedmaster Pro do not hold the movement to the case, but the movement to the enlargement ring. The ring and movement simply sits inside the case, and the whole unit is pressed into the case and held there by the pressure of the case back on the dust cover. So don't flip the watch over dial up once the case back has been removed, because the movement will move inside the case, and this can cause dial damage. Also, when prying the dust cover off, always pry from the stem side of the movement, not the other side.
And please don't handle anything, including the dust cover, with bare fingers. I see finger prints etched in these and this is why. Finger cots or a glove are recommended.
Lastly when replacing the back, if you don't replace the case back seal, then at least apply some silicone grease to the O-ring (a small amount will do, you just need a thin film). The grease does not help the watch seal as many think, at least not directly. The grease allows the case back to slide over the seal as it is being tightened so the seal does not tear or stretch.
Hope this helps.
Cheers, Al