Ron, I saw the coolest chess set on Pinterest the other day. The board's squares were all "dished" leaving a rounded bottom for each square. The chess pieces all had a rounded bottom to match (more or less) the curve in the squares. I didn't keep a link but a search for chess sets on Pinterest should produce a pic.
The pieces on this set were not elaborate and I would think they would be fairly easy to turn or carve. They may also need a weight in the bottom to keep them from tilting?
Good luck, Ralph