The surfaces of neutron stars are sources of strongly polarized soft X-rays due to the presence of strong magnetic fields. Radiative transfer mediated by electron scattering and free–free absorption is central to defining local surface anisotropy and polarization signatures. Scattering transport is strongly influenced by the complicated interplay between linear and circular polarizations. This complexity has been captured in a sophisticated magnetic Thomson scattering simulation we recently developed to model the outer layers of fully ionized atmospheres in such compact objects, heretofore focusing on case studies of localized surface regions. Yet, the interpretation of observed intensity pulse profiles and their efficacy in constraining key neutron star geometry parameters is critically dependent upon adding up emission from extended surface regions. In this paper, intensity, anisotropy, and polarization characteristics from such extended atmospheres, spanning considerable ranges of magnetic colatitudes, are determined using our transport simulation. These constitute a convolution of varied properties of Stokes parameter information at disparate surface locales with different magnetic field strengths and directions relative to the local zenith. Our analysis includes full general relativistic propagation of light from the surface to an observer at infinity. The array of pulse profiles for intensity and polarization presented highlights how powerful probes of stellar geometry are possible. Significant phase-resolved polarization degrees in the range of 10%–60% are realized when summing over a variety of surface field directions. These results provide an important background for observations to be acquired by NASA’s new Imaging X-ray Polarimetry Explorer X-ray polarimetry mission.