"Exact" quantum dynamics calculations of vibrational spectra are performed for two molecular systems of widely varying dimensionality (P 2O and CH2NH), using a momentum-symmetrized Gaussian basis. This basis has been previously shown to defeat exponential scaling of computational cost with system dimensionality. The calculations were performed using the new "SwitchBLADE" black-box code, which utilizes both dimensionally independent algorithms and massive parallelization to compute very large numbers of eigenstates for any fourth-order force field potential, in a single calculation. For both molecules considered here, many thousands of vibrationally excited states were computed, to at least an " intermediate" level of accuracy (tens of wavenumbers). Future modifications to increase the accuracy to "spectroscopic" levels, along with other potential future improvements of the new code, are also discussed.