Thanks, guys!! All your descriptions are fabulous. Louise also sent me a PM describing an even easier alternative way to achieve the same not -- Louise, I'm talking up your brilliance and am going to share your trick. Hope you don't mine!
Fold scarf in half and pass one end through loop, as usual.
Instead of twisting the knot, though, simply take the remaining end, pass it over the top of the loop and then feed it through the other side.
I just tried tying it that way and the 180-degree-twist way, and my results were indeed the same.
AJ, I unfortunately can't get much benefit from pictures because I'm totally blind, but your verbal description was most informative. Thank you for that, as well as introducing us all to this fun new knot!