Here is another strategy completely. Your mesh just sucks and can't be unfolded since it's not fine and regular enough, so I've invoked a convoluted strategy to remesh it after Kangaroo MeshMachine was way too tweaky and full of failure modes, I indeed make a patch, the back to a mesh via custom mesh settings, then to a polysurface and that can be unfolded:

Is unfolding a plug-in though? Yes, it's a part of TTToolbox:

http://www.food4rhino.com/project/tttoolbox

Now if you need a simple flat NURBS surface you could get the border and make a patch again, and the patch will be undistorted, just a simple trimmed single surface.

Actually, the result above is separate little surfaces that won't fully join, but in fact join into five pieces, so I have to tweak the custom meshing to get it to really join into one polysurface, but then it STILL has bad joins:

Grasshopper is truly bad for end users since algorithms are lacking. Plug-ins were supposed to make up for that, and indeed Exact Flat exists for $27K with $5K a year maintenance fee for upgrades:

http://www.exactflat.com/store/c1/Featured_Products.html

Even with the fine meshing it's not *quite* developable (unfoldable along hinges) so there are little gaps and overlaps. Can I tease out a border curve anyway? Nope! Joining the edge curves of the joined surfaces is a mess:

And I was even wrong about remeshing being needed since your original mesh will unroll too as a polysurface:

And it works for joining properly, so my remeshing screwed it up, merely. That's a confusing glitch, actually, meaning this is not a robust system yet and you're getting lucky, but here is the border converted to a flat NURBS patch:

To make it robust you may need a slow Kangaroo or Kangaroo2 flattening via hinges and some slight elasticity added too to let those gaps stay closed while a huge force tried to flatten the faces.

I understand now that the mesh/polysurface faces are what keep it from distorting much, but the unfold algorithm of TTToolbox is primitive so just rips things apart instead of incorporating a bit of elasticity as an option.

Fabtools also has an unroll component:

http://www.grasshopper3d.com/group/fabtools

In hindsight now that I came around right back to unfold, I think you simply failed to join your mesh-derived NURBS surfaces into a polysurface?