To avoid the seaming problem, you could start with a 360-degree pano stitched together from several photos. But it's even
more fun if you start with an equirectangular projection of a spherical pano and do a
stereographic projection, especially since it's now built into Hugin.
Original equirectangular:
With stereographic mapping, becomes:
If you want to see a master of remapping, take a look on Flickr at
Seb Przd's photostream.