The natural gas sector, as a pivotal transition fuel, is fundamentally constrained by the “Energy Trilemma”—the intertwined and often competing goals of energy security, affordability, and sustainability. Current research predominantly focuses on the demand side, leaving a significant gap in understanding the synergistic dynamics within production regions, which are critical to resolving this trilemma at its source. To address this gap, this study constructs a “Safety–Economy–Green” (S-E-G) evaluation framework aligned with the trilemma’s dimensions. Utilizing panel data (2011–2021) from four major Chinese natural gas production regions (Sichuan, Chongqing, Shaanxi, and Shanxi). By integrating the Entropy Weight Method, a Coupling Coordination Model, and Kernel Density Estimation, it delineates the system’s synergistic dynamics from both temporal and regional perspectives. The key findings are as follows: (1) Significant disparities and polarization are observed in the S and G dimensions, while the E dimension shows a narrowing gap, with its peak height increasing by 177.8% and bandwidth shrinking by 64.2%. G has emerged as a constraint on overall system coupling coordination. The persistently high coupling degree—rising from 0.87 in 2011 to 0.97 in 2021 while consistently exceeding the coordination degree, which increased from 0.45 to 0.62—underscores the continued need for improvement in synergistic development. (2) The coupling coordination degree of the S-E-G system underwent a three-stage evolution: rapid improvement (2011–2013, from 0.36 to 0.58 at 7.3% annually), fluctuating adjustment (2014–2017, between 0.58 and 0.66), and finally high-level stability (2018–2021, stabilizing at 0.76–0.80). (3) Obvious regional differentiation exists: Sichuan achieved a moderate level of 0.76 by 2021, Shaanxi maintained primary coupling coordination (0.6–0.7), while Chongqing and Shanxi remained marginal, fluctuating between 0.4 and 0.6. Enhancing subsystem coordination and implementing differentiated pathways are therefore essential for these regions’ sustainable development. The study suggests promoting the sustainable development of natural gas production regions by enhancing subsystem coordination and exploring differentiated pathways, thereby providing practical guidance for the energy transition of resource-based regions.