@wes_mcgee_3d What are you trying to accomplish? If you want the closest point in the least squares sense to the lines then the location of planes intersecting the lines is totally irrelevant. The planes can be located anywhere along the lines without affecting the closest point.
If you want the point closest in the least squares sense to a set of points then that is different problem. That corresponds to the volume centroid of the points with an arbitrary but equal volume/mass assigned to each point. One way to solve for this in Rhino is to place a spheres of arbitrary radius centered at each point, and then use VolumeCentroid on the set of spheres. Make sure the spheres are all the same size and are centered on the points. The spheres can overlap as long as they are not trimmed.
As I mentioned above the center of a sphere passing through 4 points is the point equidistant from the 4 points, not the point closest to the 4 points.