As LLM agents advance rapidly in autonomy, the risk of hidden objectives that bypass safety constraints becomes increasingly plausible. Chain-of-thought (CoT) monitoring offers a key control mechanism by reading the agent's reasoning and flagging misalignment before it materializes into action, yet its reliability depends on the realism of the red-team it is stress-tested against. Existing red-teaming efforts rely on shared templates, such as casting a side task as a prerequisite, which treat the side objective as an exogenous insertion and leave task-specific, contextually grounded evasions underexplored. We therefore ask: How robust is CoT monitoring against agents that strategically conceal misalignment? To answer this, we introduce TraceMRT, an automated Trace-level Monitor Red-Teaming framework that reframes the side task as a coherent sub-goal of the primary task and searches trace-shaping strategies whose induced trajectories complete the misaligned objective while reading as natural execution. Through black-box attacks on state-of-the-art monitors such as GPT-5.2 and Claude-4.5, we reveal substantial vulnerabilities even in top models. To counter these vulnerabilities, we propose a Bayesian Trajectory Monitoring framework, integrating global context and local segment evidence to detect covert misalignment. Empirically, our method significantly consolidates monitor robustness with 0.91 AUC and 0.74 TPR@FPR=0.05.