In this paper, we propose a novel adaptive carrier sense multiple access scheme with collision avoidance (CSMA/CA) to perform efficient and reliable data transfer with increased throughput across multiple coexisting wireless body area networks (BANs) in a tiered architecture. We investigate the proposed scheme using two distributed cross-layer optimized dynamic routing techniques, i.e., shortest path routing (SPR) and cooperative multi-path routing (CMR). The channel state information from the physical layer is passed on to the network layer using an adaptive cross-layer carrier sensing mechanism between the physical and MAC layer, which adjusts the carrier sense threshold (e.g., RSSI) periodically based on the slowly-varying channel condition. An open-access experimental dataset of 'everyday' mixed-activities is used for analyzing the cross-layer optimization. Our proposed optimization using adaptive carrier sensing performs better than static carrier sensing with CSMA/CA as it reduces the continuous back-off duration and latency as well as significantly increases the throughput (in successful packets/s) by more than 50%. Adaptive CSMA/CA also shows 20% and 6% improvement over a coordinated TDMA approach with higher duty cycle for throughput and spectral efficiency, respectively, and provides acceptable packet delivery ratio and outage probability with respect to SINR.