Sorry to be redundant, but I just picked up a KME and it works better than anything else I have tried. I don't use it on a stone, however.
I use it on on auto body sand paper in progressively finer grits (1000,1500, 2000) wrapped over a 12x12 scrap piece of marble (from a kitchen and bath store). I tape the ends of the paper and then I wet it to make it lay perfectly flat. Then I start the honing process the same way it is done in the video.
By the time you get done with the 2000 grit and a few strops on a leather, my 2 blades are pretty darn sharp.