Full-duplex spoken dialogue systems promise to transform human-machine interaction from a rigid, turn-based protocol into a fluid, natural conversation. However, the central challenge to realizing this vision, managing overlapping speech, remains critically under-evaluated. We introduce Full-Duplex-Bench v1.5, the first fully automated benchmark designed to systematically probe how models behave during speech overlap. The benchmark simulates four representative overlap scenarios: user interruption, user backchannel, talking to others, and background speech. Our framework, compatible with open-source and commercial API-based models, provides a comprehensive suite of metrics analyzing categorical dialogue behaviors, stop and response latency, and prosodic adaptation. Benchmarking five state-of-the-art agents reveals two divergent strategies: a responsive approach prioritizing rapid response to user input, and a floor-holding approach that preserves conversational flow by filtering overlapping events. Our open-source framework enables practitioners to accelerate the development of robust full-duplex systems by providing the tools for reproducible evaluation.