So, I played with some parametric Bezier splines, and that went -- horribly.
:D

But it hinted at the source of the problem - the interpolated control points are
control points - NOT on the surface of the patch - so a spline based on those
doesn't touch the surface.

I got rid of the intermediate sweeps and all is well.

Ricky's off the hook.
Good job.

:)

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