OK, I'm getting a bit closer - the interior_texture was throwing me off, since
the 180 degree rotation was throwing me all off.
Here's the same diagram with the interior_texture commented out along the top
row to show the "see-through" [exterior]texture and give an easier to follow
look at the mapping.
This is indeed much closer to the expected uv-mapping, given the location of the
control points.
There's some switch-ups that occur when there are certain twists in the
X-vs-Y-first ordering, but that should be within grasp.
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