In NLP, Event Coreference Resolution (ECR) is the task of connecting event clusters that refer to the same underlying real-life event, usually via neural systems. In this work, we investigate using abductive free-text rationales (FTRs) generated by modern autoregressive LLMs as distant supervision of smaller student models for cross-document coreference (CDCR) of events. We implement novel rationale-oriented event clustering and knowledge distillation methods for event coreference scoring that leverage enriched information from the FTRs for improved CDCR without additional annotation or expensive document clustering. Our model using coreference-specific knowledge distillation achieves SOTA B³ F₁ on the ECB+ and GVC corpora and we establish a new baseline on the AIDA Phase 1 corpus. Our code can be found at https://github.com/csu-signal/llama_cdcr.