Great looking machine, Muerto! Love the artwork on the Namco/Bertolini cabs.
You should be able to carefully wet sand the front of the perspex bezel and marquee with various grits working your way up to a nice polish to get rid of the scratches, though to avoid "dips" you'll probably want to do the entire front surface. Then you can polish it up with something like Novus 2.
That would work pretty well for the marquee and bezel, though depending how bad the cig burn is it'll probably only minimize that.
I did this for some Taito Space Invaders and Nintendo DK parts and they turned out nice. I'm sure there's a good tutorial of this somewhere.

Hope that helps!
