In many countries, medical services are delivered through a multi-hospital network where a patient may have unlimited choices to different points of access to care. Due to various reasons, such a network may experience substantial workload imbalance. One way to address this challenge relies on government providing higher subsidy to incentivize patients to visit hospitals with low workload/utilization. In this research, we studied the problem of optimal government-to-patient subsidy differential (G2P-SD) policy design. We first formulated the problem with a nonlinear optimization model to minimize the total social cost (i.e., the cost of weighted wait time plus government subsidy spending) subject to the minimum workload requirement. Then we used a discrete choice model with real-world data to identify the significant influence of G2P-SD on patient hospital visit choice and numerically specified the rates of patient arrivals at a multi-hospital outpatient care network accordingly. We next developed a large-scale two-level queuing network to analyze the impact of G2P-SD on patient flows within the service network. We defined funding efficiency as a potential indicator to policy makers for effective budget allocation among various types of patients. Our study verified the effectiveness of modifying the G2P-SD policy, i.e., the total social cost is reduced by 55.99%. Furthermore, our study suggested the benefit of further tailoring the policy design with consideration of influential patient attributes, which leads to a further reduction in wait time at high-workload hospitals in our Shanghai-based case study.