Yes, but in doing so you are back to playing beyond the river, in Eskimo territory, right to where I started !
Perhaps I misunderstood you, but I thought that this was your
purpose... I tried to save a would-like-to-be crossing knot bowline from opening up, due to this weakly secured upper collar leg/tail.
The "Pretzel" was only a way to secure the second leg/tail even further - you can omit it if you wish. In general, when the tail enters into the nipping loop, one can hardly resist the temptation to pass it in between the first curve of the standing part or/and the returning eye leg.
Ring loading comes AFTER the normal loading !

If you load your knots while you have not yet tightened the collar structure very much, you will see that the second leg of the higher collar will not be able to participate in the stability of the nipping loop very much. It seems that the higher collar is more weak and less helpful to the overall integrity of the structure than the lower one, so that was the reason I turned the knot upside down.
I have not studied the crossing knot (-)bowlines as much as I believe I should had to - maybe because they are not a-la-mode in this Forum !

However, I believe they are very interesting, very robust eyeknots, which deserve a more detailed examination. The more complex nipping structure offers many "steps" and "handles" to the collar structure, which, by its turn, can be "hitched" upon it in many secure ways.
( I should also mention that, by "crossing knot" eyeknots, I tend to mean the eyeknots where the standing part cross itself in more than one points. So, by this definition, the "Eskimo" bowlines may be (-) bowlines, but they are not "proper" crossing knot eyeknots...

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