Two concurrent factors challenge the evaluation of large-scale cache networks: complex algorithmic interactions, which are hardly represented by analytical models, and catalog/network size, which limits the scalability of event-driven simulations. To solve these limitations, we propose a new hybrid technique, that we colloquially refer to as ModelGraft, which combines elements of stochastic analysis within a simulative MonteCarlo approach. In ModelGraft, large scenarios are mapped to a downscaled counterpart built upon Time-To-Live (TTL) caches, to achieve CPU and memory scalability. Additionally, a feedback loop ensures convergence to a consistent state, whose performance accurately represents those of the original system. Finally, the technique also retains simulation simplicity and flexibility, as it can be seamlessly applied to numerous forwarding, meta-caching, and replacement algorithms. We implement and make ModelGraft available as an alternative simulation engine of ccnSim. Performance evaluation shows that, with respect to classic event-driven simulation, ModelGraft gains over two orders of magnitude in both CPU time and memory complexity, while limiting accuracy loss below 2%. Ultimately, ModelGraft pushes the boundaries of the performance evaluation well beyond the limits achieved in the current state of the art, enabling the study of Internet-scale scenarios with content catalogs comprising hundreds of billions objects.