Biological invasions reshape environments and affect the ecological and economic welfare of states and communities. Such invasions advance on multiple spatial scales, complicating their control. When modeling stochastic dispersal processes, intractable likelihoods and autocorrelated data complicate parameter estimation. As with other approaches, the recent synthetic likelihood framework for stochastic models uses summary statistics to reduce this complexity; however, it additionally provides usable likelihoods, facilitating the use of existing likelihood-based machinery. Here, we extend this framework to parameterize multi-scale spatio-temporal dispersal models and compare existing and newly developed spatial summary statistics to characterize dispersal patterns. We provide general methods to evaluate potential summary statistics and present a fitting procedure that accurately estimates dispersal parameters on simulated data. Finally, we apply our methods to quantify the short and long range dispersal of Chagas disease vectors in urban Arequipa, Peru, and assess the feasibility of a purely reactive strategy to contain the invasion.