First, I think you need to flatten the input Force objects. 

Second main issue, your springs are only in one direction of the mesh. 

Third, the spring stiffness might be too high. To get more info on this part, someone else might have to help.

Your approach is complicated. Unless you really want to create things from scratch yourself, make use of Daniel Pikers components. For example you can just create the mesh the way you built it, then use the warp weft component and extract the lines.

You should also use anchors on all four corners.

However, my approach would be slightly different. I'd start with a square mesh in Rhino.

This mesh should only have one face. You can later edit it efficiently by moving its four corners / control points. Subdivision happens in GH, using a catmull clark component out of the weaverbird tab.

The above is a simple approach. Later, you can of course also start playing with separate stiffness values for the naked edge of the mesh. The warp weft component has two additional outputs. It tells you whether an edge is a naked edge or not. 

Hope that helps, if not, ask :-)

In case the subdivision is not enough, you can also subdivide the output mesh after kangaroo did the relaxation... saves some time