The underwater acoustic channel continues to present significant challenges to efficient throughput performance of underwater acoustic sensor networks (UASNs) in varying scenarios. As a result, cross-layer approaches that explore joint PHY/MAC strategies are worthy of further exploration. We consider a recent high-speed OFDM modem and propose a new cross-layer solution based on modified CSMA/CA, for a canonical star network topology with few nodes (the most common scenario in UASNs). Some innovations to an adaptive OFDM PHY link are developed to jointly select the modulation, convolutional coding and frequency diversity order (different transmission modes) for matching varying channel conditions. Additionally, receiver logic that disambiguates the cause of packet loss between a) that caused by channel vs. b) that due to collisions is used to modify the ARQ/backoff logic for retransmissions with CSMA/CA random access. Simulation results reveal that the cross-layer design can effectively increase network throughput.