I'm finding that there is a very noticeable difference when this object is rendered with a crease angle of 50 (upper) and a crease angle of 60 (lower).  I did not think that crease angle even had an effect on shadows, and I can't explain the blockiness of the raytraced shadows in the upper image.  The faces in question don't actually appear "flat" until lowering the crease value into the 20s, so I have no idea why a value of 50 (or even 59) looks so diffrent from 60.    

This is really frustrating, as what works best for the shadows doesn't look right for the reflections and vice versa. 

(Blue fog is a result of saving as png and using wrong background color)

That is very strange. The shadow in the top image doesn't seem to match the shape of the lid that is casting it. Have you tried rendering with "Smooth polygons" checked in the render settings? I don't know if that will help, but it's another option.

The geometry looks like it's smoothing, turn off PolySmooth in your render settings and at the prop level and then see what happens while still trying different crease angle settings.

Crease angle can be set in general preferences.
Smoothing has to be turned ON in the render settings.

And crease angle has to be set for each group in the object file in the parameters palette.

Where did you change what?

Quote - Smoothing has to be turned ON in the render settings.

That's not necessarily true, depending on what is on the stage or being rendered.

Geometry smoothing is off (it would balloon the object), and crease angle was set in object properties on per-object basis.

The apparent mismatch of the shadow to the geometry is what really caught my attention.  The ray traced shadow seems too close to the depth map preview shadow's blockiness.

Unless I am mistaken or something has changed, crease angle doesn't affect object smoothing (which would be useful).  Smoothing creates geometry, crease angle affects (phong?) interpolation of surface normals at rendertime.

Quote - Geometry smoothing is off (it would balloon the object), and crease angle was set in object properties on per-object basis.

I should clarify that both smoothing and crease angle were set on a per-object basis.  It makes it easier to mix and match props and figures that can be smoothed with those that should not.