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This work presents results from simulations of the 14 July 2000 ("Bastille Day") solar proton event. We used the Energetic Particle Radiation Environment Model (EPREM) and the CORona-HELiosphere (CORHEL) software suite within the SPE Threat Assessment Tool (STAT) framework to model proton acceleration to GeV energies due to the passage of a CME through the low solar corona, and compared the model results to GOES-08 observations. The coupled simulation models particle acceleration from 1 to 20 $R_\odot$, after which it models only particle transport. The simulation roughly reproduces the peak event fluxes, and timing and spatial location of the energetic particle event. While peak fluxes and overall variation within the first few hours of the simulation agree well with observations, the modeled CME moves beyond the inner simulation boundary after several hours. The model therefore accurately describes the acceleration processes in the low corona and resolves the sites of most rapid acceleration close to the Sun. Plots of integral flux envelopes from multiple simulated observers near Earth further improve the comparison to observations and increase potential for predicting solar particle events. Broken-power-law fits to fluence spectra agree with diffusive acceleration theory over the low energy range. Over the high energy range, they demonstrate the variability in acceleration rate and mirror the inter-event variability observed solar-cycle 23 GLEs. We discuss ways to improve STAT predictions, including using corrected GOES energy bins and computing fits to the seed spectrum. This paper demonstrates a predictive tool for simulating low-coronal SEP acceleration.