Dan, I've seen this hinted at elsewhere - tying a sheet bend to an eye - but I don't see how to do that under tension.
It's a matter of relative forces to pull tight & hold.
IFFFF one can hold the tension with one hand,
then the forming of the
sheet bend's wrap & tuck
can be made, and with some reduction of size of
the loop this forms, then pulling hard on the tail
to set it --with some tension yield from the now-released
SPart. So it's a question of working with something
that can be so tensioned & held in hand; it's not a
general solution.
More general, and incorporating the
rolling hitchqua "tautline hitch" --well, that name says is!-- is doing
the pull-through-eye tensioning and tying off the tail
with the hitch. So, like your 2HHitches solution but
now with the hitching coming just anywhere out along
the tensioned line pulled through the eye. (And sometimes
I put in a *guard*
half-hitch to take off some force on
the working end.)
I suppose one drawback of the rolling hitch method is that it falls apart is tension is released
?! No, that hitch should stay tied; there are ways
to help with that (stopper in the tail, or other).
YMMV per materials.
--dl*
====