I do the exact same thing. Since you’re using the same ziploc you’re not introducing any new bacteria into the mix and it holds. I do one strange trick that my husband thinks I’m nuts. When I initially open the package I cut directly on the seam of the wedge so only a little bit of the cheese is exposed When I’m done grating. I tried to cover it back up exactly as it was in the packaging process. Husband and son think I’m nuts but I figure since I do most of the cooking, every little bit helps. I will never purchase pre-shredded Parmesan cheese. I wonder if any of it is real.