We present a forward-modeling framework using the Bayesian inference tool Starfish and cloudless Sonora-Bobcat model atmospheres to analyze low-resolution ($Rapprox80-250$) near-infrared ($1.0-2.5$ $mu$m) spectra of T dwarfs. Our approach infers effective temperatures, surface gravities, metallicities, radii, and masses, and by accounting for uncertainties from model interpolation and correlated residuals due to instrumental effects and modeling systematics, produces more realistic parameter posteriors than traditional ($chi^2$-based) spectral-fitting analyses. We validate our framework by fitting the model atmospheres themselves and finding negligible offsets between derived and input parameters. We apply our methodology to three well-known benchmark late-T dwarfs, HD 3651B, GJ 570D, and Ross 458C, using both solar and non-solar metallicity atmospheric models. We also derive these benchmarks physical properties using their bolometric luminosities, their primary stars ages and metallicities, and Sonora-Bobcat evolutionary models. Assuming the evolutionary-based parameters are more robust, we find our atmospheric-based, forward-modeling analysis produces two outcomes. For HD 3615B and GJ 570D, spectral fits provide accurate $T_{rm eff}$ and $R$ but underestimated $log{g}$ (by $approx1.2$ dex) and $Z$ (by $approx0.35$ dex), likely due to the systematics from modeling the potassium line profiles. For Ross 458C, spectral fits provide accurate $log{g}$ and $Z$ but overestimated $T_{rm eff}$ (by $approx120$ K) and underestimated $R$ (by $approx1.6times$), likely because our model atmospheres lack clouds, reduced vertical temperature gradients, or disequilibrium processes. Finally, the spectroscopically inferred masses of these benchmarks are all considerably underestimated.
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