Obtaining a high-quality interaction model with associated uncertainties is essential for neutrino experiments studying oscillations, nuclear scattering processes, or both. As a primary input to the MicroBooNE experiment's next generation of neutrino cross section measurements and its flagship investigation of the MiniBooNE low-energy excess, we present a new tune of the charged-current pionless (CC0p) interaction cross section via the two major contributing processes - charged-current quasielastic and multinucleon interaction models - within version 3.0.6 of the GENIE neutrino event generator. Parameters in these models are tuned to muon neutrino CC0p cross section data obtained by the T2K experiment, which provides an independent set of neutrino interactions with a neutrino flux in a similar energy range to MicroBooNE's neutrino beam. Although the fit is to muon neutrino data, the information carries over to electron neutrino simulation because the same underlying models are used in GENIE. A number of novel fit parameters were developed for this work, and the optimal parameters were chosen from existing and new sets. We choose to fit four parameters that have not previously been constrained by theory or data. Thus, this will be called a theory-driven tune. The result is an improved match to the T2K CC0p data with more well-motivated uncertainties based on the fit.