We present a model for the rotational evolution of a young, solar-mass star interacting magnetically with an accretion disk. As in a previous paper (Paper I), the model includes changes in the star's mass and radius as it descends the Hayashi track, a decreasing accretion rate, and a prescription for the angular momentum transfer between the star and disk. Paper I concluded that, for the relatively strong magnetic coupling expected in real systems, additional processes are necessary to explain the existence of slowly rotating pre-main-sequence stars. In the present paper, we extend the stellar spin model to include the effect of a spin-down torque that arises from an accretion-powered stellar wind. For a range of magnetic field strengths, accretion rates, initial spin rates, and mass outflow rates, the modeled stars exhibit rotation periods within the range of 1--10 days in the age range of 1--3 Myr. This range coincides with the bulk of the observed rotation periods, with the slow rotators corresponding to stars with the lowest accretion rates, strongest magnetic fields, and/or highest stellar wind mass outflow rates. We also make a direct, quantitative comparison between the accretion-powered stellar wind scenario and the two types of disk-locking models (namely the X-wind and Ghosh & Lamb type models) and identify some remaining theoretical issues for understanding young star spins.