For overcoming this limitation (stationary camera) of all panorama software, try making photosynths, rather than panoramas. The Photosynth website does host both types of photography, but the only way to currently create photosynths is with the Windows app.
You can use a Photoshop plugin or Microsoft Research's ICE panorama stitcher on Windows or the Photosynth mobile panorama app to upload panoramas, but only Windows has an app to make photosynths.
To make a good synth, instead of a panorama, it is actually very important to move the camera all around your subject. For lots more detail, try this discussion: http://bit.ly/sinkorsynth