Currently, China’s expressway revenue and expenditure imbalance problem is serious. The development of an “Expressway Derivative Economy” (EDE) helps address expressway deficits, ensuring the expressway's sustainable operation. The “Expressway + Logistics Distribution” (ELD) mode is a crucial form of the EDE and enhances expressway traffic flow and asset income. However, the cooperation mechanism among stakeholders remains unclear, hindering the widespread promotion of this mode. This study designs two ELD modes and elaborates on their respective advantages. Therefore, a three-party evolutionary game model involving the government, expressway groups, and logistics enterprises is established. Government “land-use-right” grant and tax incentive policies are formulated to explore the cooperation mechanism among stakeholders. The results indicate that both government “land-use-right” grant and tax incentive policies positively influence the positive evolution of the system. However, when the government “land-use-right” grants reach a high level, the willingness of logistics enterprises to choose entry will decrease due to resource crowding. Comparatively, a higher-level “land-use-right” grant policy significantly enhances the role of government tax incentive policy in promoting the positive development of the system. During tight government funding, it is a feasible policy to prioritize expressway groups by providing more tax incentives. The findings provide theoretical guidance for promoting the ELD mode.