Update My question is a duplicate of Extracting centerline of a Complex-Polygon in PostGIS/Python (though if anyone has a programmatic solution - that is, not ArcGIS but rather Py, C, Java, etc. - I would be interested).
The rough idea was to perform a negative buffer that exceeded the diameter of the geometry at any given point. This does not work, though, and leads to an empty geometry.
How might I perform a geometric operation on a shape so as to impute its centermost points? Is some form of negative buffering a reasonable approach? Or, is there a more well-word path to achieving the spline of such geometries?