Regarding the polarizing issue, I'll throw in my two cents. I think both camps are correct, to a degree. Perfect polarization does indeed eliminate glare spots and does increase apparent saturation and contrast, so your photo may be accurate to the technical composition of the original's color and density, but maybe not to the way the painting is perceived.
In the past I had a painter client who used a vicious amount of texture and varnish. Double polarizing raised the contrast so high that the film literally could not maintain detail in both ends of the tonal scale. I had to resort to "flashing" the film--exposing it to a plain white board at a 3-4 stop underexposure--to bring the contrast back under control. Now, whenever someone calls me about photographing their art, my first question is not, "How big is it?" or, "Is it in a frame?" No, the first thing I ask is, "What's the surface like?"
Digital photography has made this sort of thing easier, but I'd still rather stay away from the world of impasto.
As for a possible, simpler, solution to the glare problem you already have, perhaps you could rely on the fact that your hot spots are probably the only part of the file that measure 255-255-255. Use that fact to make selections and then...well, then I'm not sure. Maybe...
-increase the selected areas by a few pixels, and feather them
-invert the selection
-Ctrl (or Cmnd)-J to put the selection on a new layer
-at this point you'll have a Background layer, and a layer above which has holes in it where the hotspots happened
-on the Background layer (or, more safely, a copy of it) apply a Median filter (Filter>>Noise>>Median). I think that's the one you'd want because it would blur the layer in such a way as to push the darker, good, values into the light, hot, areas.
-The darkened values would appear under the holes in your top layer.
-With some experimentation as too what numbers to apply to the different steps, I think you could fill in the holes pretty well.
For what it's worth.