Data-sovereignty regulations increasingly require public institutions to deploy open-source, on-premise LLM agents that chain multiple tool-calls across live government APIs. However, open-source models consistently underperform in this multi-step setting, and no existing benchmark measures the gap. We introduce the Korean Open Public API Benchmark KOPA-Bench, comprising 145 real-world tasks on which open-source models underperform. To close this gap, we present EDGE, an Execution-grounded Dynamic Graph for tool-calling data synthEsis driven by live execution. EDGE builds a graph of how each tool’s output can feed another’s input, keeps only the links that succeed when actually called against the live APIs, and traverses these verified links to synthesize executable multi-step trajectories. Fine-tuned via GRPO on the resulting dataset, our 9B model nearly matches the untuned 27B model from the same family, improving substantially not only on KOPA-Bench but also on the BFCL benchmark.