Ok, ok Richard, here is where it gets rich and the blows may begin to fly because of the strong feelings attached with the way we do things and how we learned those ways, rather by tradition like you having learned from your father who learned from his father etc..., or someone like me who has had to struggle alone from a point of ignorance at no little cost in time and money to say the least. So we are invested in how we each do it and can be expected to have strong reasons for backing it up. But I divorce now my writing self from my woodworking self for the sake of discussions, (ha ha ha don't believe it for a second). I should say I'm not totally convinced there is one right way to do these things, maybe that's not possible given so many complicated variables involved.

But first I wanted to write something about your fantasy scenario from above. Such a massive piece of wood could only be squared from the ground at least initially. In the past for practical reasons and because I am an l.w. I have squared up in two stages first removing bulk waste in a very rough way simply to get a timber to the point I could manage to situate it better. I would also notch it with two cutting the v grooves at one time standing on the ground at the side. How you going to score or notch from above with the bottom side of the timber three feet below your feet? Then with a splitting axe, not a maul, who knows,maybe even a double bitted, with a long handle start rough wasting as quick as possible and once it was reduced, get it to where I could work with more precision and pleasure, though that rough wasting would be fun too.

I guess to be fair the question over grip could be turned around to ask how the ones using the grip the other way round, inside hand at the back, manage it that way. Let me put this drawing up just so that we are both on the same page, knowing that the axe and way you go about squaring the log are different from the way I go about it.

This is one of the standard modern images used widely around the internet and in a number of publications to include the Axe Book from Gränsfors Bruk, the tool catalogue from Dick has also printed this image usually with their own explanations accompanying. I pulled it from a Swedish document about historical carpentry work. It's very interesting mostly for what's omitted.
And here am I going at it another time in that stance I like so much except for maybe not so low.
I wonder what could be said about these shots other than one way is right and one way is wrong. To me there is a certain logic and consistency underlying a grip that allows a posture that is square to the working surface and the forces exerted to be in one line with our desire to get the line vertical with a minimal exertion.

Got to leave it there for now Richard and get myself back out to the workshop.