PSR J1306-40 is a millisecond pulsar (MSP) binary with a non-degenerate companion in an unusually long ~1.097 day orbit. We present new optical photometry and spectroscopy of this system, and model these data to constrain fundamental properties of the binary such as the component masses and distance. The optical data imply a minimum neutron star mass of 1.75+/-0.09M_{sun}_ (1{sigma}) and a high, nearly edge-on inclination. The light curves suggest a large hot spot on the companion, suggestive of a portion of the pulsar wind being channeled to the stellar surface by the magnetic field of the secondary, mediated via an intrabinary shock. The H{alpha} line profiles switch rapidly from emission to absorption near the companion inferior conjunction, consistent with an eclipse of the compact emission region at these phases. At our optically inferred distance of 4.7+/-0.5kpc, the X-ray luminosity is ~10^33^erg/s, brighter than nearly all known redbacks in the pulsar state. The long-period, subgiant-like secondary, and luminous X-ray emission suggest this system may be part of the expanding class of MSP binaries that are progenitors to typical field pulsar-white dwarf binaries.