BEFORE
AFTER
I did the old sharpie treatment. First I sprayed a layer of armor all to get it cleaned and coated. Then i took a fine tip black sharpie and dotted along the scratch...rubbing it in as I go. Don't dot too much, otherwise you'll see a black line instead of a blended scratch. Eventually it blends the scratch to the point where you can't even notice it. I'd try this first before risking heating the plastic.
There was an even deeper one on the right door panel...and it worked great.