I remember back in my TV days when the tube gunning technician had a returned tube with a deep scratch. He used jeweler's rouge and managed to get it out well. The screen was as smooth as anything but there was a noticeable 'dent'
I would have been concerned about the strength of the tube with this deep depression but it was obvioulsy useless for vision! Personally I would have no fear of polishing out light scratches.
Seriously though - I have used Solvol Autosol and similar for scratches on car screens. I once had a really frightening experience with a plank blowing off a lorry and hitting my windscreen flat! It left a dent
which took some polishing out!