I read somewhere - can't remember where, because I read about this movie a lot lately - that the continous color changes were due to the fact that often a single shot/scene was filmed during different moment of the day, or in different days and also location...
I agree that a perfect single setting to regrade the whole movie does not exist; but I surely prefer this to the original color grading...
About flesh tones; all the settings I used preserve them, apart just a bit of saturation less, as the original grading was a little bit "pumped" in this.
Tell me which shot do you like to see (30 sec) and I'll encode it; meanwhile, if you want to share your color settings, I'll be more than happy to test and eventually, with your permission of course, use them for the project!