The multiplayer online battle arena (MOBA) genre has gained significant popularity and economic success, attracting considerable research interest within the Human-Computer Interaction community. Enhancing the gaming experience requires a deep understanding of player behavior, and a crucial aspect of MOBA games is matchmaking, which aims to assemble teams of comparable skill levels. However, existing matchmaking systems often neglect important factors such as players' position preferences and team assignment, resulting in imbalanced matches and reduced player satisfaction. To address these limitations, this paper proposes a novel framework called CUPID, which introduces a novel process called ``re-matchmaking'' to optimize team and position assignments to improve both fairness and player satisfaction. CUPID incorporates a pre-filtering step to ensure a minimum level of matchmaking quality, followed by a pre-match win-rate prediction model that evaluates the fairness of potential assignments. By simultaneously considering players' position satisfaction and game fairness, CUPID aims to provide an enhanced matchmaking experience. Extensive experiments were conducted on two large-scale, real-world MOBA datasets to validate the effectiveness of CUPID. The results surpass all existing state-of-the-art baselines, with an average relative improvement of 7.18% in terms of win prediction accuracy. Furthermore, CUPID has been successfully deployed in a popular online mobile MOBA game. The deployment resulted in significant improvements in match fairness and player satisfaction, as evidenced by critical Human-Computer Interaction (HCI) metrics covering usability, accessibility, and engagement, observed through A/B testing. To the best of our knowledge, CUPID is the first re-matchmaking system designed specifically for large-scale MOBA games.