<< This image is atypical in that it is displayed in aRGB colorspace even though its for web viewing. See below: >>

It is obvious that there are multitudes of 'less than intuitive' aspects that were preventing accurate Color Checker rendering for me.

I had assumed that Adobe was using a straight curve with a film-like roll-off above and below the gray patches.
The latter might be true but the curve from ‘paper white’ to ‘shadow black’ is certainly not straight, at least when using Adobe Standard and Process2012 in ACR CC2015.

However, the biggest faux pas is thinking that a color balance will accurately correct colors under a variety of lighting. I had been experimenting with inexpensive Halogen work lights and that lighting is abysmal, color wise.
Metamerism was eating me alive. Just going outside, even at 3:30 in the winter afternoon, provided MUCH, MUCH more accurate color rendition.

While the 'exposure compensation' was modest and no 'contrast correction' was needed to set the paper white and shadow black ‘end points’ there was still a huge curve needed to wring any sort of accuracy to the middle grays.
While not awe inspiring, the rest of the chart is reasonable for the first time under this 6600 K lighting... 'reasonable' being a moving target.

This lighting is closer to D50 now, which is actually what the chart is designed to be used at (or presumably what the numbers are calibrated to).
I do NOT assume that my custom 'curve' has enough points to be valid and where I set those points is sloppy. I've addressed this in other attempts but with similar output results.

Even though the Color Checker chart is traditionally measured in sRGB or LAB this Jpeg is in aRGB because that is my workflow. Here I can compare my results to ideal ColorChecker2005 colorspace corrected aRGB patch numbers.