Since true communities within real-world networks are rarely known, synthetic networks with planted ground truths are valuable for evaluating the performance of community detection methods. Of the synthetic network generation tools available, Stochastic Block Models (SBMs) produce networks with ground truth clusters that well approximate input parameters from real-world networks and clusterings. However, we show that SBMs can produce disconnected ground truth clusters, even when given parameters from clusterings where all clusters are connected. Here we describe the REalistic Cluster Connectivity Simulator (RECCS), a technique that modifies an SBM synthetic network to improve the fit to a given clustered real-world network with respect to edge connectivity within clusters, while maintaining the good fit with respect to other network and cluster statistics. Using real-world networks up to 13.9 million nodes in size, we show that RECCS, applied to stochastic block models, results in synthetic networks that have a better fit to cluster edge connectivity than unmodified SBMs, while providing roughly the same quality fit for other network and clustering parameters as unmodified SBMs.