It's not clear what materials you're working with in trying to tie
some quickly secure binding: you mention both "ropes" and
some "triangle bandage, rolled up". ??
Here's a quick idea: make an Overhand Noose in one end
(this might be regarded as a "Slip Knot", but the difference
is that the "slipping" part --what moves-- is the main line,
not the end);
insert the opposite end through the noose eye, and even
make a 2nd insertion (somewhat *surgeon*ish, this),
and then pull back on this inserted end to pull thing tight,
which should capsize the twist in the noose eye such that
the eye is now a full round turn (double turn) around the
end, AND further tightening will tighten this noose's turn's
grip on the end (which you could at some point tie off
in a bona fide Slip Knot (end moving, for easier untying),
to completely prevent it from sliding back through the
noose's grip.
NB: one can reeve the end around either side of the noose's
eye legs --i.e., around the side leading to the Overhand knot,
or around the side that is leading out to the main rope binding.
The difference will be whether this short coil is loaded like
a Rolling Hitch vs. the ProhGrip (Blake's; also Klemheist) hitch.
Both seem to work (though in one case with here some soft-laid
3/8" nylon, the lay is grossly distorted. YMMV.
.:. You want quick, simple, effective; EMT folks & hospitals
are (too) happy to cut bindings later (I lost a rope belt after
an accident, alas). This knot should be able to be manually
further tightened or loosened, one hand grasping the knot
body, the other pulling the inserted end whichever way is
desired. No rope need be harmed in this binding!
Your thoughts about the vulnerability of the double twist
that your instructor is using are right on target: that requires
backing which might never adequately be there, or, as you
remark, might disappear with some movement & shifting.
(I have it from a doctor acquaintance that surgeons in fact
never use this so-called knot -- much like the Dutch Navy
probably hasn't got some different bowline, or Stevedores
their own stopper, or ... -- knotting, a world of myths!)
--dl*
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ps: In anticipation of things to come:
No, the Gleipnir is nota workable solution here!