Identifying central nodes using closeness centrality is a critical task in analyzing large-scale complex networks, yet its decentralized computation remains challenging due to high communication overhead. Existing distributed approximation techniques, such as pruning, often fail to fully mitigate the cost of exchanging numerous data packets in large network settings. In this paper, we introduce a novel enhancement to the distributed pruning method specifically designed to overcome this communication bottleneck. Our core contribution is a technique that leverages multi-packet messaging, allowing nodes to batch and transmit larger, consolidated data blocks. This approach significantly reduces the number of exchanged messages and minimizes data loss without compromising the accuracy of the centrality estimates. We demonstrate that our multi-packet approach substantially outperforms the original pruning technique in both message efficiency (fewer overall messages) and computation time, preserving the core approximation properties of the baseline method. While we observe a manageable trade-off in increased per-node memory usage and local overhead, our findings show that this is outweighed by the gains in communication efficiency, particularly for very large networks and complex packet structures. Our work offers a more scalable and efficient solution for decentralized closeness centrality computation, promising a significant step forward for large-scale network analysis.