Effective relevance modeling is crucial for e-commerce search, as it aligns search results with user intent and enhances customer experience. Recent work has leveraged large language models (LLMs) to address the limitations of traditional relevance models, especially for long-tail and ambiguous queries. By incorporating Chain-of-Thought (CoT) reasoning, these approaches improve both accuracy and interpretability through multi-step reasoning. However, two key limitations remain: (1) most existing approaches rely on single-perspective CoT reasoning, which fails to capture the multifaceted nature of e-commerce relevance (e.g., user intent vs. attribute-level matching vs. business-specific rules); and (2) although CoT-enhanced LLM's offer rich reasoning capabilities, their high inference latency necessitates knowledge distillation for real-time deployment, yet current distillation methods discard the CoT rationale structure at inference, using it as a transient auxiliary signal and forfeiting its reasoning utility. To address these challenges, we propose a novel framework that better exploits CoT semantics throughout the optimization pipeline. Specifically, the teacher model leverages Multi-Perspective CoT (MPCoT) to generate diverse rationales and combines Supervised Fine-Tuning (SFT) with Direct Preference Optimization (DPO) to construct a more robust reasoner. For distillation, we introduce Latent Reasoning Knowledge Distillation (LRKD), which endows a student model with a lightweight inference-time latent reasoning extractor, allowing efficient and low-latency internalization of the LLM's sophisticated reasoning capabilities. Evaluated in offline experiments and online A/B tests on an e-commerce search advertising platform serving tens of millions of users daily, our method delivers significant offline gains, showing clear benefits in both commercial performance and user experience.