Try "Softscrub". It's made to clean fine porcelain and it's a very mild abrasive. Also Meguiar's Mirror Glaze for auto polishing works well.
Any fine abrasive is fine. Put some on the wet crystal, rub heck out of it with your thumb, rinse, dry, enjoy.
I had some MASSIVE gouges on my 1665 and used a knife to scrape away plastic until the level of the gouges was reached, then I used Ajax cleanser (coarse abrasive) to smooth it a little, then used Softscrub (very mild abrasive) to achieve the final gloss finish.
Easy squeasy.