Thanks for the reply, and I might just be misunderstanding you, but...what I'm trying to do sounds like the exact opposite of what you're describing. That is, I don't want to make a 3D model from photos. Instead, I want to take photos OF a 3D model and turn them into a stitched 2D composite photo.

You mention, "Looking from the center of the sphere outwards (a panorama) is more or less the same problem as looking at the center of the sphere." That doesn't seem correct to me because (again, I'm likely just misunderstanding you, so I apologize for the confusion) when viewing a sphere from any angle you will only ever see half of it, whereas looking at a panorama you will see the entire thing. That's the problem into which I keep running: I can easily take a single photo of a sphere and stretch that into an equirectangular image, but it doesn't cover the entire surface of the sphere I'm shooting, therefore the single-image version would always be incomplete.