In the interest of addressing mobile users' Quality of Experience (QoE) demands and ensuring good Quality of Service (QoS) for innovative, high-performing services, the forthcoming generation of wireless networks is integrating Multi-access Edge Computing (MEC), Software Defined Mobile Networks (SDMN), and Cloud Radio Access Networks (C-RAN). These technologies aim to enhance performance and assure QoS in light of the growing complexity of telecom networks. They also aim to address escalating traffic and user demands for higher bitrate speeds. This paper explores resource allocation across a wireless network empowered by MEC, SDMN, and C-RAN technologies to facilitate high-quality adaptive video streams. We introduce a MEC server collaboration-based Cross-Layer Bitrate Allocation algorithm that leverages user and RAN MAC layer data, including Reference Signal Received Power (RSRP), traffic behaviors, and preferred video quality, to optimize users' QoE while minimizing backhaul traffic by reducing caching requests from the Central Cloud, located in operator backhaul. Addressing a mixed-integer nonlinear programming challenge, we consider radio resource availability constraints and MEC servers' storage and transcoding capacities of MEC servers. The proposed algorithm, termed Cross-Layer MEC-Enabled Bitrate Allocation (CLMEBA), aims to enhance users' QoE by minimizing the discrepancy between the achievable throughput at the MAC layer and the allocated bit rate for video frames at the application layer while also reducing backhaul traffic through MEC server collaboration. Compared with a baseline scheme, our algorithm realizes a 22.36% enhancement in system utilization rate, a 18.11% improvement in video quality, and a 49.87% reduction in backhaul traffic.