The unphysical flow of zero-point energy (ZPE) in classical trajectory calculations is a consequence of the fact that the classical phase-space distribution may enter regions of phase space that correspond to a violation of the uncertainty principle. To restrict the classically accessible phase space, we employ a reduced ZPE gamma epsilon(ZP), whereby the quantum correction gamma accounts for the fraction of ZPE included. This ansatz is based on the theoretical framework given in Paper I [G. Stock and U. Muller, J. Chem. Phys. 111, 65 (1999), preceding paper], which provides a general connection between the level density of a system and its relaxation behavior. In particular, the theory establishes various criteria which allows us to explicitly calculate the quantum correction gamma. By construction, this strategy assures that the classical calculation attains the correct long-time values and, as a special case thereof, that the ZPE is treated properly. As a stringent test of this concept, a recently introduced classical description of nonadiabatic quantum dynamics is adopted [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], which facilitates a classical treatment of discrete quantum degrees of freedom through a mapping of discrete onto continuous variables. Resulting in negative population probabilities, the quasiclassical implementation of this theory significantly suffers from spurious flow of ZPE. Employing various molecular model systems including multimode models with conically intersecting potential-energy surfaces as well as several spin-boson-type models with an Ohmic bath, detailed numerical studies are presented. In particular, it is shown, that the ZPE problem indeed vanishes, if the quantum correction gamma is chosen according to the criteria established in Paper I. Moreover, the complete time evolution of the classical simulations is found to be in good agreement with exact quantum-mechanical calculations. Based on these studies, the general applicability of the method, the performance of the classical description of nonadiabatic quantum dynamics, as well as various issues concerning classical and quantum ergodicity are discussed.