Cross-polarization is usually required for oil paintings to kill the reflections. It's normally so efficient that you may even need to dial down contrast and saturation.
Some pigments reproduce well, others not. I suspect some of them reflect in the IR range, which means the sensor is affected but the eye not. Then you need to adjust in post. Don't make the mistake of assuming you can get a perfect colorimetric match. You won't, and you don't need to. If you try, the result will quickly lose its internal "logic" and consistency and will not look credible.
Think equivalent color, not identical. Colors that work within the whole, and have the same visual impact. That will be accepted as a faithful reproduction. Each specific pigment has its own unique "personality" and with experience you'll recognize them and know how to reproduce them in a credible way.
It's imperative that you use a good monitor, properly calibrated to match intended print/output conditions. You need to know that what you see is what you get. Beyond that, color management won't help you.
IME camera profiling only makes matters worse, because precision isn't nearly high enough with only 24 patches in a standard color checker chart. You'd need a lot more, and specific to the pigments used. I always use the Adobe Standard profile in Lr. Be careful with the Hue/sat adjustments in both Lr and PS; they tend to break up image integrity with banding and artifacts. Selective Color in Photoshop is better.
