One possible variation is to use an overhand knot on each end rather than simply using a turn around the bowstring. This gives the knot more consistent bulk all the way around.
Do not forget that this hitch is a friction gripping hitch.
If it is not going to be loaded lengthwise ( and this particular application does not load it like this ), there is no point of having more riding turns than the minimum number required to secure / lock the ends. When a round turn of the rope goes "over" another, it loses its contact with the surface of the pole - and we need as much contact area as we can have. The very interesting variation you present, although it, too, has 4 wraps, it will grip the surface of the pole along a much smaller area than the original hitch. As shown in the video, the 4 parallel semi-circular arcs at the "back" side are doing a great job, a feature that is absent in your variation. I feel that the added security / locking of the ends it offers, cost too much in contact area.
Having said that, I believe that your variation might be better when we have a lengthwise pull. The "cross gartering" of the round turns will help them grip the pole harder, when they will be elongated. One can also embrace the ends
in a Strangle-way, instead of a Constrictor-way. The Strangle has the advantage that the ends are leaving the knot s nub parallel to the axis of the pole - so, if the one end is loaded, during a lengthwise pull, it will not change orientation, and it will not deform the knot s nub ( as it might happen with a Constrictor, loaded lengthwise...).