Easy for me to see your adze with a socket like your hatchet, just the edge turned 90 degrees. There's a blade smith south of me who does exactly that.
Kestrel puts out a 12 page booklet of information, photographs and handle template drawings, called "Adzes and Ends". I used Kestrel patterns for both the D-adze (minus the snail) and the Baby Sitka elbow adze. I have both a Kestrel Sitka blade and wood for a handle to assemble a full-sized Sitka elbow adze.
Bill Holm took it upon himself, many decades ago, to analyze the geometry found in the art, carvings and tools common to the First Nation of the Pacific Northwest. His text book is as exciting as watchin the mortar set around bricks.
Besides the Holm Constant for hand position, there's another dimension to be considered, one that I call the "Kestrel Constant." This is the size diameter of the handle, which can be fitted like the handle sizes on tennis racquets.
Palm up, fist grip, the tips of your second and third fingers should just touch the fat ball of your thumb. I started with a fat, soft, wood handle and cut it down 1/4" at a time. It became obvious what was comfortable. From 1" to 3/4" is my range. 7/8", I can swing all day and it isn't a "death grip", too skinny or too fat.
If you look closely at the adze handles, you can see just enough shadow to show where the hand grip has been thinned a little. I've seen dozens of elbow adzes, the handles are never made with much thought to the geometry.
I learned that making crooked knives. The one knife with a 3/4" handle still sports the laminate I made from strips of rosewood and mahogany. I always said to myself that I'd make a new handle. Lazy sod that I am, I bulked it up with VetWrap bandage and let a go at that.
If you got this far, you must be bored to tears. I'll make up a slurp of "grandpa's vitamins" and build my supper.