This paper describes the application of a relatively simple, but computationally tractable, "particle-on-a-sphere" (POS) model for quantum-mechanical calculation of large-amplitude, H atom dynamics in polyatomic hydrides (XH(n)), based on radially relaxed, two-dimensional angular motion of H atoms on the surface of a sphere. This work focuses on systems with many degrees of freedom, i.e., XH(4) (eight dimensional) and XH(5) (ten dimensional), with corresponding molecular analogs of CH(4) and CH(5) (+) and is applicable to rovibrationally excited states with J> or =0. A pairwise-additive potential fit for CH(5) (+), which yields remarkable agreement with geometries, energies, and barrier heights on the full-dimensional surface of Brown et al. [J. Chem. Phys. 121, 4105 (2004)] is presented. Comparisons with experimental data and diffusion quantum Monte Carlo (DMC) methods test convergence for the POS model and provide insight into multidimensional quantum rovibrational dynamics. In particular, POS energy-level patterns for a series of scaled CH(5) (+) potentials indicate an absence of strong tunneling behavior, consistent with the highly delocalized wave functions, large zero-point energies, and small interconversion barriers noted in previous DMC studies of Brown et al.