Analyses of parasocial cues in live-stream chats require accurate, efficient, and scalable annotation. However, manual annotation is tedious, and large language models (LLMs) often make mistakes when applying subjective, discourse-dependent labels. This study proposes Context-aware Batching for Stream Annotation with LLMs (CaBSALLM), an efficient pipeline that incorporates lightweight conversational context and a novel dynamic batching method to improve throughput and scalability. Compared with state-of-the-art pipelines, this generalizable approach is significantly more time- and cost-efficient while achieving comparable or better predictive performance and agreement.