Variational and diffusion Monte Carlo results are presented for the ground states of several SF6HeN clusters in the range N = 1-499. The diffusion Monte Carlo computations are well converged, yielding an expected accuracy in the energy well under 1%. Computations are performed employing both an isotropic and an anisotropic He-SF6 interaction potential. Novel trial wave functions are used to describe both the shell structure of these clusters and the anisotropy arising from the potential. The ground state helium densities show the SF6 located at the cluster center, inducing a large degree of localization and a shell-like structure in the surrounding helium. Although the full potential causes a large degree of anisotropy in the helium density, general characteristics such as the energy and size are not greatly affected by the potential anisotropy. Finally, we compute spectral shifts for the nu3 SF6 vibration due to the instantaneous dipole-induced dipole mechanism and compare with recent experiments. We find a red shift which for N less-than-or-equal-to 111 increases with N to a maximum value of 0.93 cm-1, with a width of 0.25 cm-1, at N = 111.