We demonstrate the extraction of excited rovibrational state energies for quantum systems with up to 15 dimensions, using the recently developed projection operator imaginary time spectral evolution (POITSE) method. The technique is applied to a series of model van der Waals complexes of the form AB-X-n, n = 1-3, with heavy AB and a weakly bound, light atom X. The selectivity of several types of molecule-fixed and space-fixed projectors and their relationship to the nature of the accessible excited states are studied by making comparison with discrete variable-finite basis representation (DVR-FBR) calculations for n=1. These also allow identification of excitations dominant in ground state infrared absorptions. The results suggest a propensity for space-fixed projectors to access states where the angular momentum of the diatomic AB dominates the overall angular momentum, while molecule-fixed projectors access primarily bending and stretching modes. The relevance of this observation for the interpretation of the rovibrational spectra of molecules embedded in large liquid helium clusters is discussed.