Large language models (LLMs) has been widely used for automated negotiation, but their high computational cost and privacy risks limit deployment in privacy-sensitive, on-device settings such as mobile assistants or rescue robots. Small language models (SLMs) offer a viable alternative, yet struggle with the complex emotional dynamics of high-stakes negotiation. We introduces EmoMAS, a Bayesian multi-agent framework that transforms emotional decision-making from reactive to strategic. EmoMAS leverages a Bayesian orchestrator to coordinate three specialized agents: game-theoretic, reinforcement learning, and psychological coherence models. The system fuses their real-time insights to optimize emotional state transitions while continuously updating agent reliability based on negotiation feedback. This mixture-of-agents architecture enables online strategy learning without pre-training. We further introduce four high-stakes, edge-deployable negotiation benchmarks across debt, healthcare, emergency response, and educational domains. Through extensive agent-to-agent simulations across all benchmarks, both SLMs and LLMs equipped with EmoMAS consistently surpass all baseline models in negotiation performance while balancing ethical behavior. These results show that strategic emotional intelligence is also the key driver of negotiation success. By treating emotional expression as a strategic variable within a Bayesian multi-agent optimization framework, EmoMAS establishes a new paradigm for effective, private, and adaptive negotiation AI suitable for high-stakes edge deployment.