I’ve figured out why I couldn’t get either the D4 or the D800E to white balance to the screen shots. It was pure cockpit error on my part. I misread the manuals for both cameras, which are virtually identical with respect to white balancing. I thought you could get the camera to compute and store white balance coefficients from a photograph stored on the cameras’ removable memory cards. Instead, when you ask the camera to use a stored photograph for white balance, it merely copies the white balance coefficients from that photograph into a preset.
It seems the only way to have the cameras compute a set of white balance coefficients from an image is to go through the “Direct Measurement” procedure, where the camera makes an exposure, computes the white balance coefficients from that exposure, stores those coefficients in a presser, and does not write the image to the memory card.
Once I realized the error of my ways, it was easy to get the white balance coefficients to better than +/- 2% with both cameras. One exposure with the coarse target, one with the fine target, white balance to the solid color, and make one exposure of the solid color to check the coefficients.
Everything now works as expected. So I’m done, right? No so fast. There is an improvement to the gridded-search approach in the works, and I’m working on an iterative approach based upon Newton’s method. I also need to write everything up so that it flows logically, instead of following the way I worked on the problem, with all the twists, turns, and false steps.