We present a follow-up analysis examining the dynamics and structures of 41 massive, large star-forming galaxies at z ∼ 0.67 - 2.45 using both ionized and molecular gas kinematics. We fit the galaxy dynamics with models consisting of a bulge, a thick, turbulent disk, and an NFW dark matter halo, using code that fully forward-models the kinematics, including all observational and instrumental effects. We explore the parameter space using Markov Chain Monte Carlo (MCMC) sampling, including priors based on stellar and gas masses and disk sizes. We fit the full sample using extracted 1D kinematic profiles. For a subset of 14 well-resolved galaxies, we also fit the 2D kinematics. The MCMC approach robustly confirms the results from least-squares fitting presented in Paper I: the sample galaxies tend to be baryon-rich on galactic scales (within one effective radius). The 1D and 2D MCMC results are also in good agreement for the subset, demonstrating that much of the galaxy dynamical information is captured along the major axis. The 2D kinematics are more affected by the presence of noncircular motions, which we illustrate by constructing a toy model with constant inflow for one galaxy that exhibits residual signatures consistent with radial motions. This analysis, together with results from Paper I and other studies, strengthens the finding that massive, star-forming galaxies at z ∼ 1 - 2 are baryon-dominated on galactic scales, with lower dark matter fractions toward higher baryonic surface densities. Finally, we present details of the kinematic fitting code used in this analysis.