Do you have a weblog entry about your panoramic tripod head? It would be great to get a look at it and hear about the construction process.
My first question is whether your tripod head rotates the camera around the camera's lens/imaging plane or rotates around some other part of the camera.
It might be that ICE would still make a stitching mistake with a perfect set of input photos, but the problem with traditional panorama stitching is that the stitchers don't handle parallax well, meaning that if your camera's lens is traveling in an orbit with a diameter of, say, nine inches, the difference in perspective (small though it may be) will result in foreground objects and background objects being different distances from each other in your various input photos. When the panorama stitcher attempts to align all the photos to any particular corner, this means that other portions of the photos don't line up.