The better technique for making flat surfaces, without scraping, is to lap the three plates against one another. Actually grind them, using a sequence of increasingly-finer abrasives until you end up with jewelers' rouge. This is the surface-plate version of mirror-grinding; you'll end up with three optically flat plates, smooth to within a fraction of a wavelength.

Or you can glue a piece of 1200-grit sandpaper to a piece of float-glass (which is made by floating molten glass on molten tin) and have something that's good enough for sharpening jointer knives and plane irons.