The broadening of the hydrogen lines during flares is thought to result from increased charge (electron, proton) density in the flare chromosphere. However, disagreements between theory and modeling prescriptions have precluded an accurate diagnostic of the degree of ionization and compression resulting from flare heating in the chromosphere. To resolve this issue, we have incorporated the unified theory of electric pressure broadening of the hydrogen lines into the non-LTE radiative transfer code RH. This broadening prescription produces a much more realistic spectrum of the quiescent, A0 star Vega compared to the analytic approximations used as a damping parameter in the Voigt profiles. We test recent radiative-hydrodynamic (RHD) simulations of the atmospheric response to high nonthermal electron beam fluxes with the new broadening prescription and find that the Balmer lines are over-broadened at the densest times in the simulations. Adding many simultaneously heated and cooling model loops as a "multithread" model improves the agreement with the observations. We revisit the three-component phenomenological flare model of the YZ CMi Megaflare using recent and new RHD models. The evolution of the broadening, line flux ratios, and continuum flux ratios are well-reproduced by a multithread model with high-flux nonthermal electron beam heating, an extended decay phase model, and a "hot spot" atmosphere heated by an ultrarelativistic electron beam with reasonable filling factors: 0.1%, 1%, and 0.1% of the visible stellar hemisphere, respectively. The new modeling motivates future work to understand the origin of the extended gradual phase emission. ; Comment: 31 pages, 13 figures, 2 tables, accepted for publication in the Astrophysical Journal