The "Construct Minimum Distance Line" tool currently only works using line/arc linear elements. This function would be exponentially more powerful if it would work with Mesh and Solid elements, the same way that the "Measure Distance" tool works with the "Minimum Between" option.
In case the solids are already interest advanced analysis with point and plane will be in need. Please also help consider how to implement the minimum distance (somethings related to "perpendicular") between a given point and a planar shape. (In VBA, that is called Point3dProjectToPlane3d)