Dark matter-only simulations predict that dark matter halos have steep, cuspy inner density profiles, while observations of dwarf galaxies find a range of inner slopes that are often much shallower. There is debate whether this discrepancy can be explained by baryonic feedback or if it may require modified dark matter models. In Paper 1 of this series, we obtained high-resolution integral field H$alpha$ observations for 26 dwarf galaxies with $M_*=10^{8.1}-10^{9.7}textrm{M}_odot$. We derived rotation curves from our observations, which we use here to construct mass models. We model the total mass distribution as the sum of a generalized Navarro-Frenk-White (NFW) dark matter halo and the stellar and gaseous components. Our analysis of the slope of the dark matter density profile focuses on the inner 300-800 pc, chosen based on the resolution of our data and the region resolved by modern hydrodynamical simulations. The inner slope measured using ionized and molecular gas tracers is consistent, and it is additionally robust to the choice of stellar mass-to-light ratio. We find a range of dark matter profiles, including both cored and cuspy slopes, with an average of $rho_{rm DM}sim r^{-0.74pm 0.07}$, shallower than the NFW profile, but steeper than those typically observed for lower-mass galaxies with $M_*sim 10^{7.5}textrm{M}_odot$. Simulations that reproduce the observed slopes in those lower-mass galaxies also produce slopes that are too shallow for galaxies in our mass range. We therefore conclude that supernova feedback models do not yet provide a fully satisfactory explanation for the observed trend in dark matter slopes.
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