The most effective way to tackle this project would be to start in a 3D app like Maya, Cinema 4D or Blender, unfold the UV map and export the distorted texture.
Experimenting in Photoshop CC, I applied this
as a texture map to a simple 3D sphere:
Then, using the (new in 2014)
3D > Generate UVs... command like this
I came up with a texture map and UV wireframe that allowed me, with a couple of extra steps using the Magic Wand and a Layer Mask, to extract this mapping from the modified texture file:
Photoshop isn't the best tool (or even a good tool) for this job, but this indicates the general approach to creating a wrappable, pre-distorted template. Rather than trying to create the template directly as a 2D file, apply it to a 3D object as a texture map, then unfold the map.
Using well-chosen seams and UV unwrapping in Maya or a similar 3D application, you would be able to create whatever slices you needed (and much more effectively than this simple Photoshop demonstration).