Urban public safety operations face persistent challenges in managing high service demand under limited resources. Rapid detection and coordinated response to gunfire incidents are particularly critical, as they require data-driven decision support for patrol scheduling, resource allocation, and operational planning. This study leverages multi-year ShotSpotter acoustic detection data from Washington, D.C. (2014--2020) to move beyond descriptive hotspot analysis toward causal modeling of performance outcomes. First, Exploratory Data Analysis (EDA) identifies distinct temporal rhythms---including nighttime surges, weekend variability, and clustering in high-incidence districts---as well as long-term seasonal trends. Building on these findings, a Structural Equation Model (SEM) is developed to capture three latent constructs: Operational Load (incident intensity, temporal concentration, clustering severity), Response Efficiency (system acknowledgment and in-district confirmation), and Strategic Readiness (district-level adaptability). Using district--week aggregates from 2019--2020, Partial Least Squares SEM (PLS-SEM) and covariance-based SEM (CB-SEM) demonstrate that higher operational load reduces response efficiency, but that strategic readiness moderates this effect by buffering efficiency losses. By integrating exploratory analytics with structural modeling, this paper advances methodological understanding of SEM in public safety research and provides practical insights for patrol deployment, district staging, and adaptive staffing policies to enhance resilience in high-demand environments.