This paper proposes RCMEN, a solution for Concurrent Multipath Transfer (CMT) of Raptor-Coded (RC) Protocol Data Units (PDU) in a Multi-Access 6G Edge Network (MEN) to provide low-latency and reliable transmission for 6G User Equipment (UE) and Data Network (DN). While 3GPP Release 16 aims to improve the reliability of a single service based on CMT, replication-based reliability causes high resource and signaling overhead, and asymmetric bandwidth and latency lead to excessive latency. RCMEN addresses these issues by distributing data across multiple PDU sessions and using a queue-aware variable-block-length Raptor encoder to optimize resource utilization under random arrivals. We analyze RCMEN’s delay-reliability performance using the Constrained Markov Decision Process (CMDP), reliability is guaranteed by the reliability function, which takes the amount of data sent as a parameter. Through Linear Programming, we obtain the optimal delay-reliability trade-off and optimize delay metrics for two classical RCMEN. Experiments show that both classical RCMEN optimize the long-tail distribution of latency while ensuring reliability, with the entire system being compatible with the current 5G network infrastructure.