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I don't know what the diameter on a Snapple bottle is but typical Omote are 6-7mm measured up from the edge. Your diamond tool will make contact and take off metal on 1 +/- mm of the Omote per pass....

Snapple bottles have a near perfect round for most Omotes. Get some two-way tape or two-way 1/16 weather stripping and a 3X2 piece of 320 W/D sandpaper, adhere the sandpaper to the bottle and reshape...