Variational transition state theory (VTST) is used to calculate rate constants for a model proton transfer reaction in a polar solvent. We start from an explicit description of the reacting solute in a solvent, and we model the effects of solvation on the reaction dynamics by a generalized Langevin equation (GLE) for the solute. In this description, the effects of solvation on the reaction energetics are included in the potential of mean force, and dynamical, or nonequilibrium, solvation is included by solvent friction. The GLE solvation dynamics are approximated by a collection of harmonic oscillators that are linearly coupled to the coordinates of the reacting system. This approach is applied to a model developed by Azzouz and Borgis [J. Chem. Phys. 98, 7361 (1993)] to represent proton transfer in a phenol-amine complex in liquid methyl chloride. In particular, semiclassical VTST, including multidimensional tunneling contributions, is applied to this model with three explicit solute coordinates and a multioscillator GLE description of solvation to calculate rate constants. We compare our computed rate constants and H/D kinetic isotope effects to previous calculations using other approximate dynamical theories, including approaches based on one-dimensional models, molecular dynamics with quantum transitions, and path integrals. By examining a systematic sequence of 18 different sets of approximations, we clarify some of the factors (such as classical vibrations, harmonic approximations, quantum character of reaction-coordinate motion, and nonequilibrium solvation) that contribute to the different predictions of various approximation schemes in the literature.