We consider an extension to discrete-space, continuous-time models for animal movement that have previously been presented in the literature. The extension from a continuous-time Markov formulation to a continuous-time semi-Markov formulation allows for the inclusion of temporally dynamic habitat conditions as well as temporally changing movement responses by animals to that environment. We show that, with only a little additional consideration, the Poisson likelihood calculation for the Markov version can still be used within the multiple imputation framework commonly employed for analysis of telemetry data. In addition, we consider a Bayesian model selection methodology within the imputation framework. The model selection method uses a Laplace approximation to the posterior model probability to provide a computationally feasible approach. The full methodology is then used to analyze movements of 15 weaned northern fur seal (Callorhinus ursinus) pups with respect to surface winds, geostrophic currents and sea surface temperature. The highest posterior model probabilities belonged to those models containing only winds and current; SST was not a significant factor for modeling their movement.