I am talking about repeating the wrap that occurs in step two in the image below,
before working the working end through the top loop again.
It seems to me as though it would provide a more secure finish
due to the multiple wraps around its standing part,
much like a slide-and-grip hitch, though I never see it used
- for good reason, perhaps?
Any and all input is appreciated!
BB ("Better Bowline"?

),
you're using "standing part" too loosely; we've come to compress
it into "SPart" and by that mean that part (or two) of a knot that
has full load --the "main line" leading into an eye knot, e.g..
And so what you're proposing to wrap isn't the SPart but the
"returning eye leg" (Agent_Smith's term).
IMO, a problem with the
Yosemite bwl. is that in wrapping
ONE strand --1dia turn-- it asks too much of often firm kernmantle
rope, which will resist bending so sharply.
What you propose, however, has been done my me for wrapping
both legs of the eye; and the result is akin to the binding
seen in the
strangle/blood knot, and, yes, does give good
slack-security as one would expect. Tying becomes a little more
tedious, but hardly terrible.
Harry Asher introduced a
bowline variation he named
"the Brummychan bowline" (I THINK that's it) in which
such wraps come around the SPart in making the (thus elaborate)
collar.
--dl*
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