This study evaluates advanced natural language processing (NLP) techniques to enhance crash data quality by mining crash narratives, using secondary crash identification in Kentucky as a case study. Drawing from 16,656 manually reviewed narratives from 2015-2022, with 3,803 confirmed secondary crashes, we compare three model classes: zero-shot open-source large language models (LLMs) (LLaMA3:70B, DeepSeek-R1:70B, Qwen3:32B, Gemma3:27B); fine-tuned transformers (BERT, DistilBERT, RoBERTa, XLNet, Longformer); and traditional logistic regression as baseline. Models were calibrated on 2015-2021 data and tested on 1,771 narratives from 2022. Fine-tuned transformers achieved superior performance, with RoBERTa yielding the highest F1-score (0.90) and accuracy (95%). Zero-shot LLaMA3:70B reached a comparable F1 of 0.86 but required 139 minutes of inference; the logistic baseline lagged well behind (F1:0.66). LLMs excelled in recall for some variants (e.g., GEMMA3:27B at 0.94) but incurred high computational costs (up to 723 minutes for DeepSeek-R1:70B), while fine-tuned models processed the test set in seconds after brief training. Further analysis indicated that mid-sized LLMs (e.g., DeepSeek-R1:32B) can rival larger counterparts in performance while reducing runtime, suggesting opportunities for optimized deployments. Results highlight trade-offs between accuracy, efficiency, and data requirements, with fine-tuned transformer models balancing precision and recall effectively on Kentucky data. Practical deployment considerations emphasize privacy-preserving local deployment, ensemble approaches for improved accuracy, and incremental processing for scalability, providing a replicable scheme for enhancing crash-data quality with advanced NLP.