I am almost the avatar for cheapskate-ness and will find ways to save money almost anywhere. With this said, I can't see your solution is better than wet and dry paper on a flat surface.

For really neglected natural stones (where wet and dry would take too long to make it worthwhile) i have a super-cheap 500 grit sharpening stone that i bought for $5 which i use. Draw a grid with pencil on the natural stone, place on top of the hone of death and rub until the lines are all gone. Admittedly I rarely have a hone that is so bad that this is necessary but it does seem to have work well.