"ABOK #1253" works for me here.
The knot in the original post should not have "Constrictor" in its naming.
(Note that ABOK doesn't call it a Constrictor either.)
This knot cannot be tied in the bight.
Second, this knot does not fall apart when you slip it off the end of an object.
These are two important features that I consider to be synonymous with the Constrictor brand.
Note that a Strangle Knot cannot be tied in the bight.
So, perhaps the knot here is better described as a more symmetric Double Strangle Knot.
Hmmm, rather than two, I see only the one aspect, put into
reciprocal behaviors (TIB).
Your arguments have some merit, but you miss the essential element of the Constrictor :
The way and degree that the tails are twisted around each other under the riding turn(s)
( differently, and more, than in the Strangle[r] ). So, ...
The fact that some knot can be tied in the bight and some not, is not always important.
We do not often use the Constrictor as we use the pile hitch. It is a very tight hitch, that is its main function.
I concur in X.'s noting K's point, yet resisting that and leaning
towards "constrictor" naming for the reasons given above.
(But I classify it NOT as a hitch, but as a
binder --both ends are
untensioned; all tension is in the knotted material around some object
(which suggests a difference with the
strangle (no 'r') binder when
it is devoid an object, perhaps serving qua
stopper (as e.g. is
promoted in rockclimbing, and there named
"double overhand").
In any case, are we agreed that the #1253 is in some sense "double"?
The
strangle series, e.g., can be seen as beginning only with
a
double overhand --getting thus the
single overwrap
(riding turn, a security element), and progressing with additional such
wraps as desired --and, i.p., I use the variations that usually include
an additional *twist* of the ends beneath some 4-8 overwraps,
depending upon material. (Egads, though, this then confounds
the simple nomenclature of matching overwraps count with the
"strangle" modifiers "double, treble, quadruple ..." and a direct
relationship to
overhands --so should call for some kind of
indicator of the twist count, as well.)
Similarly, the
constrictor can be *built up* with additional overwraps.
Knot4U, do you concur in that? --e.g., that beyond
double constrictor(meaning #1252, for the moment!), come
treble/triple,
quadruple, ...
versions of the binder? (To my mind, though, they don't build up so
nicely as does the
strangle series.) (Ashley stops at "double"
--perhaps he saw no need in then common materials to go further--;
but we can project beyond that, by a simple tying algorithm.)
And this comes back --now, in K.'s favor, we might suggest-- to show
another contrast with the
#1253 "d.c." : that it does
not lead to any
obvious
"triple c.", and only rather dubiously to a
"quad.c." !!
For the manner in which the riding turns lay into each other
in a sort of *opposition* rather than *repetition* doesn't indicate
a place for
one (three (five))) additional turn(s)_ --no, they must
come in even numbers to maintain the balance of this opposition!
.:. Well, that is thought to ponder for further exploration, in the
face of which, I think it's time to go seek a nibble of something.

--dl*
====
ps: Has it been noted that if the
double constrictor (#1252)
is brought off of the object and laid riding-turns-down on a table,
folding the out turns back down and (lifting off of the table) then
brought together (180deg from their
c. orientation) so that
the 3rd/central turn remains pointing up, that one has then a
gleipnir version!?