We extend previous work on the minimal D-term inflation model modified by right-handed (RH) sneutrino fields to include additional inflaton-sector supergravity corrections and two-field inflation effects. We show that supergravity corrections simultaneously allow ns to be within 3-year Wilkinson Microwave Anisotropy Probe limits and the cosmic string contribution to the cosmic microwave background (CMB) power spectrum to be less than 5%. For gauge coupling g<=1, the CMB contribution from cosmic strings is predicted to be at least 1% while the spectral index is predicted to be less than 0.968 for a CMB string contribution less than 5%. Treating the inflaton-RH sneutrino system as a two-field inflation model, we show that the time-dependence of the RH sneutrino field strongly modifies the single-field results for values of RH sneutrino mass mPhi>0.1H. The running spectral index is alpha[approximate]-0.0002 when mPhi<0.1H but increases to positive values as mPhi/H increases, with alpha>0.008 for mPhi>1.0H.