Just out of curiosity: what about a sheet of good quality sandpaper, of an appropriately fine grit, laid on top of a sheet of glass? That would seem to provide the equivalent of a very large stone, with a very flat surface, at a very low cost.
(Note: for my pocket knives, I use a medium and a hard Arkansas stone, so I'm not really a Philistine. But I've never seen the equivalent in a size large enough to use on kitchen knives.)