Thanks for the replies so far. Looks like ReprojectImage would have been good, but it's not for a Mac (and I'm not sure it would be able to deal with multiple overlapping views instead of just two hemispheres 180 degrees apart). The NASA G Projector looks very cool for trying projections once I have a file. And Lingon, I had also thought of ways to do it by hand: basically trace out meridians and circles of latitude on the globe, then use one of the graticules available on this site or elsewhere and draw it in by hand, mapping by eye from the grid on the globe to the graticule on the flat screen.

But I'm still holding out for a lazy way! There are after all many programs that will take multiple images from the same viewpoint and stitch them together into a spherical panorama... viewed from the inside! I need the same but viewed from the outside. Probably just needs one bit flipped in the software :-)