Jim, the book I referred to earlier is “Techniques of Spiral Work”, by Stuart Mortimer.
It is a detailed exposition on laying out and cutting open and closed spirals by hand, on cylinders and open shapes (ie bowls, vases).
But the principles are equally applicable to the router lathe.
When one sees some of what he achieves (truly inspirational), I start thinking of either investing the time in learning to do it by hand, or looking for a more sophisticated router lathe. For example, he splits bines into two at some point on the turning, eg starts with three turns and ends with six.
There are examples that you could adapt to your chess table. An intriguing one is an open spiral with a solid cylindrical core, in a contrasting wood.