So using just control edges as in mesh 4, along with a suitable crease angle of course, seems the be the polygon-lightest (about 4 times as many vertices/edges/faces as my initial mesh 1) answer to the mesh part of this problem.

Now to investigate the causes of the black shadowy meshline-related artefacts - even though EldritchCellar has already explained them

This time I've zoomed in on mesh 4 (note: the control edges are approximately an inch away from the main edges), and I've set the shader to give a fixed +0.5 inch displacement. Here's what I get with a few selected shadow, AO and IDL settings:

IDL splotchiness and ray-traced shadows seem to be the main cause of artefacts here, exactly as EC said. The AO artefacts are less obvious.

The duodecagonal (12-sided) nature of the disc-with-a-hole is quite clear. Although the smoothing rounds out the original edges, it's now the control edges that are making the 12-sided nature stand out. But in the "Cough ! Ahem !" post above, with an uneven displacement this seemed to be quitenicely obscured.

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The 3Dcheapskate* occasionally posts sensible stuff. Usually by accident. And it usually uses Poser 11, with units set to inches. Except when it's using Poser 6 or PP2014, or when its units are set to PNU or something else.
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