Off-grid green electricity-to-hydrogen and hydrogen-to-ammonia systems represent an important pathway for renewable energy consumption and low-carbon clean development. However, the inherent intermittency and instability characteristics of wind and solar power generation negatively affect the stable operation and production efficiency of the system. To address the matching challenges between renewable energy volatility and synthetic ammonia load characteristics under off-grid conditions, this paper proposes an optimal scheduling strategy considering the coordination of electrolyzer clusters and energy storage systems. In response to the process constraints of the 8-h regulation cycle of synthetic ammonia plants, a mixed-integer programming model is constructed with the objective of maximizing system net revenue. Through collaborative optimization of multi-column electrolyzer hierarchical start-stop control and bidirectional power regulation of energy storage, dynamic matching between hydrogen supply and ammonia synthesis demand is achieved. Results demonstrate that compared to conventional scheduling approaches, the proposed strategy increases annual system revenue by 3.36%, reduces power curtailment rate by 7.72%, improves electrolyzer utilization rate by 3.3%, and enables highly stable operation of the synthetic ammonia plant within cycles. The research findings provide theoretical support for constructing efficient and stable off-grid green ammonia production systems.