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Try sanding and don't be afraid. Just try to spread out your sanding strokes so as not to optically distort the crystal. Basically just avoid concentrating on one spot. I'm not so sure doing this with an unmounted crystal is such a great idea tho. I prefer mounted on the watch with masking tape around the case edges so nothing gets inside the crystal. Once you get dust/debris inside and attempt to wipe the inside clean it's hard to get things "crystal" clear again.
Thanks for the suggestions, my approach was also mask, sand + polish - but many of the compounds can't be found internationally, Menzerna products however are widely available in this part of the world as they are for automotives - so this is a review on a test crystal for those who are in search for alternatives
I go 800, 2000, 5000, 7000 - but I doubt whether 7000 does any good, if the sandpaper piece is smaller than the crystal, the edges of the paper leaves stroke marks larger than 7000 grit - so the next time I have a go, I'll likely do a quick 800 without going too deep, 2000, then Menzerna 400, 5000, and Menzerna 3500
Sometimes you'll need to remove the crystal tough as there'll be rust between the crystal and the case, in the second picture you can see a reverse rolled masking tape holding the crystal in place, it prevents compounds from getting inside the crystal
I think both approaches have their ups and downs, but I too avoid removing crystals whenever I can
In the long run considering trying Menzerna's final polish too