Photographing paintings, what light mods to use and what how to set up linear polarizing filters?

You should attach the Linear polarizer filter gels to the flash, ideally with barndoors. This will achieve the maximum effect. You may have to change their angle, as you do to the camera's circular polarizer.

You can not put the light source with a polarizer into a softbox nor bounce it off of a surface as doing so will alter the polarization once again, returning glare properties.

I'm a professional artist, and I photograph my paintings by using a daylight LED lamp above the easel pointing down on the painting, and the camera higher than the painting and angled down. This removes all the glare from texture and/or varnish. I then use perspective control in Photoshop to adjust the image back to its correct perspective. Hope this helps.