There's an article on grinding/polishing thin mirrors at Newport Glass' website (newportglass.com) that recommends working with the mirror on the bottom, supported on carpeting. Having the mirror on the bottom would also prevent any thermal heating from your hands, which could also produce zones. You didn't mention whether you were using Pyrex or plate glass.

I don't have any experience with thin mirrors, but I agree with Bob-you don't want the strokes extremely short. I've gotten into trouble every time I tried strokes less than about 1-1/2".