Effective ground station selection is critical for low Earth orbiting (LEO) satellite constellations to minimize operational costs, maximize data downlink volume, and reduce communication gaps between access windows. Traditional ground station selection typically begins by choosing from a fixed set of locations offered by Ground Station-as-a-Service (GSaaS) providers, which helps reduce the problem scope to optimizing locations over existing infrastructure. However, finding a globally optimal solution for stations using existing mixed-integer programming methods quickly becomes intractable at scale, especially when considering multiple providers and large satellite constellations. To address this issue, we introduce a scalable, hierarchical framework that decomposes the global selection problem into single-satellite, short time-window subproblems. Optimal station choices from each subproblem are clustered to identify consistently high-value locations across all decomposed cases. Cluster-level sets are then matched back to the closest GSaaS candidate sites to produce a globally feasible solution. This approach enables scalable coordination while maintaining near-optimal performance. We evaluate our method's performance on synthetic Walker-Star test cases (1-10 satellites, 1-10 stations), achieving solutions within 95% of the global IP optimum for all test cases. Real-world evaluations on Capella Space (5 satellites), ICEYE (40), and Planet's Flock (96) show that while exact IP solutions fail to scale, our framework continues to deliver high-quality site selections.