Paper Folding Maxi Pad

Hi so I'm trying to replicate this image I found

First I offseted curves and now I'm at a loss at how to move them. You can see that they don't all move "up." Nor do they all move towards the center of the object.

I think the solution is to take the surface, find the normals of the points and then move the points from that? But how can I isolate points that all into neat little curves that are found here? I'm so confused...

Here is my first shot at it I can't get the thing to even loft properly >:( 

Any help is appreciated! Thanks!