This paper presents a quasi-classical molecular dynamics study of symmetry effects on the dynamics of intramolecular electron transfer and hole transfer in a series of rigid organic donor-acceptor radical ions derived from 3 - 8, in which pairs of identical chromophores (double bonds, cyclopentadiene groups, or fulvene units) are attached to opposite ends of either an adamantane bridge or a bishomocubane bridge. The charge-shift process taking place by the most symmetrical transition structure in the mono-radical ions of these species may be either formally symmetry-allowed or symmetry-forbidden, depending on the sign of the migrating charge, the nature of the chromophore pair, and the identity of the connecting bridge. The degree to which symmetry breaking molecular vibrations affect the dynamics of charge-shift in these systems was explored using a recently developed Landau-Zener trajectory surface hopping (LZ-TSH) model. Reaction trajectories, which may hop between the ground state and the first excited state potential energy surface, of the radical ions were calculated "on the fly" using the AMI-Cl theoretical model. Canonical ensembles of approximately 200 trajectories were used to calculate frequencies of passage for the charge-shift processes in the radical ions of 3-8. It was found that frequencies of passage for the formally symmetry-forbidden charge-shift processes were only marginally smaller than those for the corresponding formally symmetry-allowed processes, implying that symmetry breaking vibrational modes are playing an important role in the charge-transfer dynamics of these systems. The identification of these symmetry breaking modes was secured by calculating secondary kinetic isotope effects and by carrying out Fourier transform analyses of reaction trajectories. Our conclusion concerning the weak role played by symmetry effects on the dynamics of charge migration processes receives support from some published experimental data.