To clear up something about my questioning the accuracy of your measuring instruments and software I was under the impression you were measuring the lights as they are with their greenish yellow white hue but I don't know what surface you pointed the Colormunki spectro to arrive at the numbers.
Your measurements are based on reflected light off something but you didn't make it clear what it was. What doesn't make sense and might be cleared up at least for me regarding the greenish yellow tint of white I see from the Cree and Walmart bulbs is maybe you were measuring off a surface these lights were lighting that has optical brighteners.
What were you measuring off of to arrive at the CRI/CCT numbers you posted?
I need to reread my books on color science. It has been several years since I studied them. Now I'm working through
Color Management for Photographers, then on to more advanced ones. Right now, I don't know how to do the L*a*b analysis you are doing. (But I do generally understand L*a*b.) I've been concentrating on the raw CRI, TLCI, Duv, and R9 measurements. And on the overall shape of the spectrums.
When I turn the lights on for photographing I don't pay attention to tints I see--cameras renders color differently than eyes do. (Especially with the Luther/Ives situation.) This is why there is CRI for human eyes and TLCI for cameras. (I think.) Clicking on a WhiBal card in the frame takes care of tints (I think).
The
ColorMunki Design spectrophotometer I use has two ports for reading. The one at the top is for reading ambient light through a diffuser. When it is set up for reading ambient light, I point it right at the light, usually six to eight inches away from the light to swamp out room reflections. I always do several measurements from slightly different angles to ensure that reflections aren't contaminating the reading. (Think of putting a microphone right next to a guitar speaker--any room reflections are too small to be meaningful.)
The bottom port on the ColorMunki is undiffused. It is for either reading reflected color (say, from printer profile charts, or a paint/fabric sample). Or for reading undiffused light (spot emission.)
The ColorMunki Design is out of production. I think that is replaced by the
i1Studio Spectrophotometer, which is a better name. Before, XRite had ColorMunki spectrophotometers and ColorMunki colorimeters (can only be used to calibrate monitors) which confused people.
Photographers use spectrophotometer for profiling printers and for measuring light. Unless you go used, the ColorMunki (or i1Studio) is the cheapest spectrophotometer you can get new. If you want to profile a printer, it comes bundled with Xrite software. Or you can use ArgyllCMS. (If you really want to profile printers the more expensive XRite options are better. But cost about three times as much.)
Even though spectrophotometers can be used to calibrate monitors, colorimeters are better. I use an i1 Display Pro to calibrate my monitors.
I put the images up at 2400x1600. If you look at the original images I attached the ColorChecker patches are larger than they are in real life so you should be able to measure them.