While price-based demand response is universally recognized as crucial for managing electric vehicle charging load, the academic literature has explored diverse mechanisms for its implementation. Prior research has revealed that applying load management schemes based on price-based demand response programs results in higher scheduling costs for low or constant-energy consumers. In addition, the inherent uncertainties involved in arrival, service requirements, market pricing and user behaviours have posed serious challenges in managing real-time charging operations. To handle these challenges, this work has addressed the charging problem at the scheduling level by analysing arrival, waiting, service and departure requests. This work proposed a mathematical model to coordinate charging to minimize the total charging cost and time for a given number of vehicles. We have developed an advanced charging algorithm and introduced a multi-leader multi-follower Stackelberg game. This strategic model ensures a Nash equilibrium, aligning the interests of consumers (vehicles) and providers (charging stations), ensuring a fair and balanced charging system. Where, charging load demand, real-time pricing, charging location, and vehicle types are used as input parameters. In the first stage, the real-time pricing obtained from the Spanish Electricity network is used to schedule the charging load, whereas the second stage is dedicated to using the proposed multi-parameter pricing for customer satisfaction and reduced cost. The results demonstrate the superior performance of our proposed scheme compared to existing approaches. Finally, we present a real-life case study to illustrate the practical effectiveness of the proposed techniques. The study underscores the potential of our approach in real-world scenarios, offering a promising avenue for enhancing efficiency and user experience in charging systems.