Hi Dan,
I applaud you for trying to decipher the picture.
Even looking at the black leather right in front of me, it's hard to tell which strand does what without looseing the structure (which is what I did).
the best I can deduce is that the lower right strand bends through righthand Strangle to go ANTI-clockwise through the key ring, and then comes back (as upper-right strand)
to Strangle the upper-left strand, which makes the Strangle just passed through.
I think this is spot on. In other words:
Strand One goes: bottom left, through DOH, bottom right, through key, upper right, then makes DOH over Strand Two
Strand Two goes: upper left, through DOH, then makes DOH over Strand One.
To clarify the structure, on the following picture, the two crossing points are where each end of the string will tie a double overhand knot.

I tried to understand your other way to use the grapevine for this problem, but wasn't sure if I got the one you were talking about. The other one I see is this, but somehow I don't think that's what you have in mind.

Thanks for your input!
With warmest regards,
Andy