The stellar halo of M31 exhibits a startling level of inhomogeneity, in which the "giant southern stream" stands out most prominently. Our previous analysis indicates that this stream, as well as several other observed features, are products of the tidal disruption of a single satellite galaxy with stellar mass ~109 M☉ less than 1 Gyr ago. Here we show that observed features of the stream and halo debris favor a cold, rotating, disklike progenitor over a dynamically hot, nonrotating one. These features include the asymmetric distribution of stars along the stream cross section and its metal-rich core/metal-poor sheath structure. We find that a disklike progenitor can also give rise to arclike features on the minor axis that resemble the recently discovered minor-axis "streams," even reproducing their lower metallicity. Although interpreted initially as new, independent tidal streams, our analysis suggests that these minor-axis streams may arise from the progenitor of the giant stream. Overall, our study points the way to a more complete reconstruction of the stream progenitor and its merger with M31, based on the emerging picture that most of the major inhomogeneities observed in the M31 halo share a common origin with the giant stream.