I've seen this topic come up occasionally, so here's my latest attempt. The pics below aren't the best but I hope they show the level of damage that the polish was able to improve upon.
I took a gamble on this piece, just came in the mail today. The seller's pics were pretty bad (blurry, at an angle) so chances were good that the slab had some scuffs. I was right.
When it arrived, it had a red smear like a grease pencil on the reverse. I cleaned that off with an alcohol pad, and the scuffs you see in this picture are after that -- it looked like someone took a pin and went back and forth over the center of the piece, like when you scratch out something on a notepad:

The product I used is PlastX -- it was recommended in some earlier threads, along with Novus Plastic Polish. I went with PlastX because I found only one formula for it on
Amazon while there are three varieties of Novus. Rather than research which one I needed, or going through all three, I just kept it simple.
I applied a pea-sized dollup directly to the slab, and some elbow grease with the microfiber cloth that came with the
Verdi-Care kit I bought last year. Rub it in, wipe it away with a clean part of the cloth. Did it again, same way. The scratches that remain are too deep for the polish to remove completely (I tried a third application, with no improvement) but overall I'm impressed with the results:

So the Plastx did a great job with the light scuffs that were obscuring the center of the piece, but didn't remove the deeper scratches near the bottom. That's not surprising, but overall it's still a much more attractive presentation than what I received. Not worth re-holdering at this point though I would have definitely considered it if the holder couldn't have been repaired at all.
Working on: Indian quarter eagles, Chinese pandas, and San Francisco tokens; upgrading my
Peace dollar and US Type sets
"Fear is the enemy of will. Will is what makes you take action; fear is what stops you, and makes you weak."
-- Sinestro to (
my avatar) Hal Jordan, "Green Lantern" (2011)