I noticed on your site that you say you do not recommend using ACR or Lightroom because they do not allow the use of camera profiles. Is this still accurate for your profiling package with the current releases of those two applications, or was this for previous versions? What about Capture One? No issue there, I assume? Adobe obviously now allows the use of camera profiles, but has an odd implementation that must recognize that the profile is appropriate, and only allows for a limited number of user selected options when it comes to profiles. Do they let ColorEyes profiles (for a Phase One back, in my case) past their gatekeeper?
I use Profoto strobes with large softboxes when I can make the reflections work (shiny, highly textured canvas can be tricky, even when the boxes are flagged off) and use extremely diffused natural light otherwise. Are you saying that you have found that strobes and two layers of fresh white diffusion on softboxes still produce color variance across a scene? I normally use a light meter, but not a color meter, although I have borrowed a friend's color meter and did not read any color shifts with my setup. Obviously, some strobes are better than others. Profoto is one of the better brands, but probably not on par with Briese (or Bron?) for consistency. I observed a slight color temperature change when I reduced the power of the strobes significantly, but that was more of an FYI experiment. I don't really mess with strobe power for art reproduction. My guess is that my need for individualized color correction is far more driven by the size of the ColorChecker color sample in profiling than variance in lighting, although I wouldn't swear it isn't possible to be some of the latter.
What tungsten source do you use? HMI?