JiK
The substances your advisers recommended for using on glass may have been best employed for polishing it rather than removing scratches. Did they mention toothpaste? The older toothpastes usually included kieselguhr ("diatomaceous earth") which is the siliceous skellies of diatoms and about the finest abrasive easily available. The advice about cleaning your teeth vigourously every time you eat something led many to get too enthusiastic with the abrasive toothpastes; this wore away the enamel, which is why most toothpastes these days are gels without the abrasive.

Cheers, Rowan