Assuming the whole thing is lacquer-sealed, you could try an acrylic primer and experiment with a softer color, knowing you can wipe the whole thing down if you're unhappy. I'd go back to the buildup artist and pay for a touchup. (Mind sharing the buildup artist's identity?) I don't think the bulk of the hair is such a big deal, it just needs to a mousy dishwater color so it "goes away" more. Wasn't it actually grey in the film? Dremeling can be done with some very tiny needle-like diamond bits, but frankly, I wouldn't. At best you'll end up with something so fragile you'll never be able to move it.
The idea of embedding the "other" Gollum in the pool, advising Smeagol to turn on Frodo, is simply out of this universe. I'd love to know how it was done -- what the print was, what the water material is that didn't disrupt the ink in the print. I know there are products made specifically for water effects, but you can also get clear resin from any resin supplier. Do you know what he used?