I reproduce artwork, paintings (oil and water color) and mixed media every so often and rely on cross polarization. I'm not an 'expert' mind you, but it seems to me that you can introduce additional saturation, naturally since you are polarizing. That's one way the appearance of the artwork may change. What I've found problematic almost half of the time, is more the camera profile's interpretation of mainly reds and blues, a problem that exists outside of the cross polarization.
My preferred practice is to view the art under optimal lighting away from the shooting area where my calibrated laptop is and visually compare the art itself to what is on screen. Whenever possible, I have the artist present as I dial in what I think are the needed adjustments in Capture One. Once in a while the artist will pipe in and ask to tweak this or that and that's when I know that when I get home to do the final processing I'll have something that we agreed upon, circumventing issues later on. The more 'picky', if you will, the artist the more I try and push for a mutual agreement on color and tone before leaving the site. Doing these tweaks on site makes it easier to bill for the time as well.
If I were shooting a single piece I might have it brought to my studio to photograph and if the artist had any issue with the product that is a lot easier to deal with than it would be with dozens of pieces.