Spatial evolutionary games are used to model large systems of interacting agents. In earlier work, a method was developed using Bayesian Networks to approximate the population dynamics in these games. One of the advantages of the Bayesian Network modeling approach is that it is possible to smoothly adjust the size of the network to get more accurate approximations. However, scaling the method up can be intractable if the number of strategies in the evolutionary game increases. In this paper, we propose a new method for computing more accurate approximations by using surrogate Bayesian Networks. Instead of computing inference on larger networks directly, we perform inference on a much smaller surrogate network extended with parameters that exploit the symmetry inherent to the domain. We learn the parameters on the surrogate network using KL-divergence as the loss function. We illustrate the value of this method empirically through a comparison on several evolutionary games.