We present progress on the translational tomography technique for measuring the three-dimensional structure of the corona from near-perihelion Wide-field Imager for Parker Solar Probe (WISPR) image sequences. Translational tomography makes use of noncircular motion of a camera to extract three-dimensional information from an optically thin subject. Parker Solar Probe (PSP) presents a special case both because of the particular structure of the corona and because of the nonlinear motion of the vantage point. We show improvements to a previous direct analytic method (described in Paper I of this series) and an alternative inversion pathway using a synthetic sequence of WISPR images. The newer method successfully reconstructs the correct locations of modeled coronal rays in a synthetic WISPR image sequence, with curvilinear camera motion modeled on the PSP orbit. We present the refined methodology and validation study, and show that the technique is ready for application to actual WISPR data.