Prior to core collapse, the neutrino emission from red supergiants (RSGs) is so large that a nearby ($\lesssim 1$kpc) RSG will become visible in current and near-future neutrino detectors. The rate of emission and the spectra of the pre-supernova (pre-SN) neutrinos from RSGs are sensitive to the temperature, density, and detailed isotopic composition of the core. During the last year of the star’s life, these properties change considerably as the nuclear burning accelerates and deleptonization begins. Uncertainties in stellar evolution modeling—including the treatment of mass loss and convective overshooting—alter the thermal conditions and composition of the RSG core as it approaches collapse, and thus one expects a consequent effect upon the pre-SN emission. In this paper we present the first study of how varying the treatment of mass loss and convective overshooting together affects the pre-collapse core properties and neutrino emission of RSGs. We use the stellar evolution instrument MESA and construct a grid of 32 RSG models with zero-age main sequence masses of $\{12,15,18,20\}$ Msun, apply the so-called "Dutch" mass-loss scheme with wind efficiencies of $\{0.2,0.4,0.8,1.0\}$, and consider two convective overshooting schemes. Our models use a large 206-isotope nuclear network in order to accurately compute the structure and composition of the star. We find that varying the treatment of mass loss and overshooting results in significant differences in core properties and the strength and timing of shell burning episodes, and that the onset of silicon shell burning leads to a localized peak in the pre-SN neutrino event rate observed by a JUNO-like detector $\sim 10$ hours to $\sim 1$ hour prior to collapse.