Quote - Here it is, no directional light - lit only by my highly-manipulated copy of that HDR.

Bingo!  That looks incredible.

I rest my case.  It may just be the angle of the shot, but the sampling in the corners of the box looks very good too.  I don't see the typical render artifacting in the corners of the interior space.  Although i'm sure it did nothing to solve that issue, it probably does as much as the addition of a direct light.   How is render time vs. standard direct light substitution?  Great results.

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Tools :  3dsmax 2015, Daz Studio 4.6, PoserPro 2012, Blender v2.74

System: Pentium QuadCore i7, under Win 8, GeForce GTX 780 / 2GB GPU.