Accurate measurements of the masses of neutron stars are necessary to test binary evolution models, and to constrain the neutron star equation of state. In pulsar binaries with no measurable post-Keplerian parameters, this requires an accurate estimate of the binary system's inclination and the radial velocity of the companion star by other means than pulsar timing. In this paper, we present the results of a new method for measuring this radial velocity using the binary synthesis code ICARUS. This method relies on constructing a model spectrum of a tidally distorted, irradiated star as viewed for a given binary configuration. This method is applied to optical spectra of the newly discovered black widow PSR J1555-2908. By modeling the optical spectroscopy alongside optical photometry, we find that the radial velocity of the companion star is 397 ± 4 km s-1 (errors quoted at 95 per cent confidence interval), as well as a binary inclination of >75°. Combined with γ-ray pulsation timing information, this gives a neutron star mass of 1.67$^{+0.15}_{-0.09}$ M⊙ and a companion mass of 0.060$^{+0.005}_{-0.003}$ M⊙, placing PSR J1555-2908 at the observed upper limit of what is considered a black widow system.