". . . the working end is coming down OVER the coils."
Yes, exactly. In the AGH, a loop part is coming down over the coils instead of the working end. After looking at it for a while, you'll eventually see how the coils themselves are reversed in each of the two hitches.
". . . for vertical poles specifically, what hitch do you know about that's better than the Mason Hitch or the Sailor's Gripping Hitch?"
Why, the "Four-Coil-Ring Fixed-Gripper Coil Hitch," of course!
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http://igkt.net/sm/index.php?topic=1839.msg12495#msg12495If it doesn't knock your socks off, then you didn't make it right.
JCS