Before sending it back to Nikon for round two I decided to run several lenses through the focus point test routine, even though it takes me about an hour each time.
Nikon 200/2 VR Every focus point was spot-on. Really, spot-on.
Nikon 24-70/2.8 (at 35mm) Almost every focus point was spot-on. The ones that were not were not off by much at all.
Sigma 35/1.4 ( the new lens ) This one had the most trouble with almost the entire center vertical strip of focus points being pretty far off. There was one other one left of bottom-center that was pretty far off. The other focus points were hit and miss, some were spot-on, some were close.
My verdict is that the camera is fine and that the lens plays a huge role in how well the lens+body AF system actually works.
So instead of sending the D800E back to Nikon I'm now considering sending the 35mm to Sigma.