Hi Norman - to clean up the four open curves, I lined up the control points according to the line segments that you see there - note the NetworkSrf would have worked without this adjustment, but this is cleaner- in general, always always always make sure that curves that are meant to be tangent are in fact tangent.
See the bits about curve continuity in the pdf file here - http://www.rhino3d.com/download/rhino/5.0/Rhino5Level2Training
It’s RhinoForWindows-centric but the info is exactly relevant to this.
Once the curves are clean, tangent, and Joined, then NetworkSrf is the command I used to make the surface.
-Pascal