Don’t dry the stones just use a lidded plastic tub and make a stone pond, keep them immersed all the time, a big time saver. After trying several mats, drawer liners etc the smooth work well until they get really wet then slide all over. The ribbed can be a little better. The bigger the sheet the dryer the underside stays and works better.

If you have space build a dedicated small table. Marble and granite stores throw small off-cuts away as they see no use for them. You may have to ask them to save a piece 2’x2’ ahead of time, it will be minimal cost. The mass helps keep it all steady when sharpening. The surface is flat and looks good.