Ah, that makes sense now. Thank you. The spheres I'm photographing are mineral spheres of different sizes, with each one being its own project. The smallest is a little less than three inches in diameter and the largest is about nine inches. They have very cool natural patterns in them than lend themselves to map-making, provided I can actually extract maps from their surfaces.

As I'm writing this, I'm running some panoramic software to test what you're saying. I'm using PT Gui. I'm not sure if it will work, but I'm happy to give it a try. If this doesn't work, I will try Waldronate's and your suggestion of running the images through a 3D program to place them on a digital sphere, then extract them to a 2D surface.