I don't use a polarizer. I do, however, put the setting on Macro and avoid using the flash. I generally consider my light source and try to accommodate the art to be oriented where the lighting helps the photo. Sometimes, with metallics, i want to get the shine or glare but it's hard to capture. Here is an older post where i had to wait for the direct sunlight at a particular time of day and then try my best to get the shots in a limited time to get the glare.
@castleberry/expectant-agog-denouement

I know it is more tricky when the medium, or paint in your case, is still wet. You could try different angles or lay the painting flat to get your shots?
I usually go back and edit my photos just a little as well. I try to increase the clarity and adjust the dark/light measures to get the best out of the images to accentuate the details a little more. I checked out your post and i didn't feel the glare was overbearing. I think we all notice our flaws a little more than others since we are the creative executives of the art.

I hope any of this response helps you out. Keep up the great work. You did great recreating that photo btw!