I think I get what you mean about “defining height as an implicit function of the curves”… change the value of Z for the mesh vertices according to their distance from each curve? How to get the blend working smoothly all around the shape where the rectangle can be close to the circle or have a large distance.
It seems hard, with this approach, to get something really nice and smooth which is why I thought of a relaxation approach.
I get creases that run from the rectangle corners to the circle and I won’t get a beautiful surface that would stand up to scrutiny under the Zebra analysis or, more importantly, my missus when she inspects the actual pieces of oak that I fasten to the ends of my stairs!
Ideally I want the entire depression to blend seamlessly into the oak it will be machined into (sandpaper can cover a multitude of sins but I hate sanding!)