Interesting thread. When I was a pup I was an Engineer at a machine builder. We had a massive granite surface plate that was certified inspection grade for flatness. One time a guy came out from the manufacturer to inspect it and re-flatten if required. The tool he used was another surface plate, about 24" x 36" with a couple of hand grips mounted on one side. After he had the high and low spots marked on the big plate, he went to work with the small plate and a tube of lapping compound. He'd slide and spin the small plate over the large in what seemed to be random patterns, although they were anything but. I remember asking him what made the plate flat. He responded "statistics", which didn't make much sense at the time, but did later. When he was done the plate was as flat as could be and had a mirror sheen.
Sharp solves all manner of problems.