i imagine it would take alot of work on a stone, even a course one.
i would personally use my belt sander to get it close, then finish with sandpaper laid on a flat plate or on a stone down to the right grit.
when you get it so thin, it gets very easy to burn out the edge even with very little pressure, so i wouldn't want to take it straight down on the belt, but would thin it alot and then take it all the way down with course sandpaper and then polish with finer sandpaper.
if you don't have a sander or anything, i would say use a really course sandpaper (if i remember correctly, vivi uses grip tape from skateboards...very course stuff!) on a flat backing. even a course stone is considerable finer than you can get high quality cloth backed sandpaper. so far, i like 50 grit cloth backed "gator grit" brand, made in sweden i think. i find it in most autobody stores or sometimes in hardware stores.
i would be interested in something like this, but don't have any to try it on. i will keep this in mind though if i run across a cheaper flat ground knife to try it out...