Frame analysis of migration news is a socially consequential task: media scholars and researchers who study how migration is narrated need tools that are not only accurate, but transparent, auditable, and accessible within the resource constraints typical of academic research groups. Existing LLM-based approaches rely on proprietary APIs and large models that raise concerns about data privacy, reproducibility and equitable access among media researchers. This work studies how a locally deployable open-source LLM can support interpretable frame analysis as an assistive tool. We introduce a Structured Chain-of-Thought (SCoT) prompting approach using Llama3-8B, enabling step-by-step justifications grounded in predefined framing categories. This structured design allows users to audit model outputs and examine alternative interpretations in a task that is inherently subjective. We evaluate our approach on a dataset of migration-related news and show that SCoT improves classification performance over zero-shot and few-shot baselines while remaining feasible on a single GPU. Then, we conduct a human-centered evaluation in which annotators assess the coherence and influence of "the model's reasoning". Results indicate that SCoT explanations are generally perceived as logical (mean score 4.1/5, though with notable variation across texts) and can prompt reflection on initial interpretations, even when disagreement persists. Our findings highlight both the potential and risks of LLM-assisted frame analysis. While structured reasoning can increase the traceability of model outputs and support critical interpretation, it can also influence human judgment in subtle ways. By enabling local deployment and emphasizing human-in-the-loop interaction, this work contributes to discussions on responsible and accessible computational tools for the study of socially impactful media narratives.