We present modeling to explore the conditions of the broad-line-emitting gas in two extreme narrow-line Seyfert 1 galaxies, using the observational results described in the first paper of this series. Photoionization modeling using CLOUDY was conducted for the broad blueshifted wind lines and the narrow, symmetric, rest-wavelength-centered disk lines separately. A broad range of physical conditions was explored for the wind component, and a figure of merit was used to quantitatively evaluate the simulation results. Of the three minima in the figure-of-merit parameter space, we favor the solution characterized by an X-ray-weak continuum, elevated abundances, a small column density (log N(H)approximate to21.4), a relatively high ionization parameter (log Uapproximate to-1.2 to -0.2), a wide range of densities (log napproximate to7-11), and a covering fraction of similar to0.15. The presence of low-ionization emission lines implies that the disk component is optically thick to the continuum, and the Si III]/C III] ratio implies a density of 10(10)-10(10.25) cm(-3). A low ionization parameter (log U=-3) is inferred for the intermediate-ionization lines, unless the continuum is "filtered'' through the wind before illuminating the intermediate-line-emitting gas, in which case log U=-2.1. The location of the emission regions was inferred from the photoionization modeling and a simple "toy'' dynamical model. A large black hole mass (1.3x10(8) M-circle dot) radiating at 11% of the Eddington luminosity is consistent with the kinematics of both the disk and wind lines, and an emission radius of similar to10(4) R-S is inferred for both. We compare these results with previous work and discuss implications.