I used a preview build of 123D Make to deconstruct the 3D model into a series of radial slices.
In case you haven't heard me rave about it before, 123D Make is a free app that does one thing and it does it extremely well. It takes any 3D model you give it and quickly lets you convert it into 2D vectors that can be cut from sheet material. At the moment, the publicly available version only allows you to perform simple slicing and to create perpendicular interlocking waffles, but future releases will allow for radial slicing, surface paneling, complex joint-making and a large handful of other cool things. With a bit of luck, these updates will appear online within the next couple of months. Watch this space!
Once I'd adjusted the radial center of my grid to align with the center of the lampshade, I fiddled with the number of slices and the material thickness until I had something that could support its own weight when made from cardboard.