There are some things developable surfaces just don't like to do. This is one of them. "Sir!" I said, "One of us must bend." And after some unpleasant words and a bit of tussling, one of us did.
Same as the screw, really, but with curves. The cross-section looks to me like a circle, rotating around an axial tube. Got this heavy gastropod vibe going. Crease pattern in PDF -- it's two pages. Easier that way.