We report on the analyses of x-ray-imaging spectroscopy data from experiments to study interspecies ion separation in direct-drive inertial-confinement-fusion experiments on the Omega laser facility. This is a continuation of recent, related research [S. C. Hsu et al., Euro Phys. Lett. 115, 65001 (2016); T. R. Joshi et al., Phys. Plasmas 24, 056305 (2017)]. The targets were argon (Ar)-doped, deuterium (D2)-filled spherical plastic shells of varying D2-Ar relative and total gas pressures. We used a time- and space-integrated spectrometer, streaked crystal spectrometer, and up to three time-gated multi-monochromatic x-ray imagers (MMIs) fielded along different lines of sight to record x-ray spectral features obtained from the implosions. The MMI data were recorded between first-shock convergence and slightly before the neutron bang time. We confirm the presence of interspecies ion separation as reported in our recent work. Extensions to the previous work include (a) the inclusion of shell mix in the data analysis, which slightly changes the amount of inferred species separation, (b) observation of species separation closer to the neutron bang time, and (c) fielding of the particle x-ray temporal diagnostic (PXTD) [H. Sio et al., Rev. Sci. Instrum. 87, 11D701 (2016)] to infer the relative timing between the neutron bang time and peak x-ray emission. Experimentally inferred species separation is compared with radiation-hydrodynamic simulations that include a multi-ion-species transport model.