The growing industrial demand for customized and cost-efficient large language models (LLMs) is fueled by the rise of vertical, domain-specific tasks and the need to optimize performance under constraints such as latency and budget. Knowledge distillation, as an efficient model compression and transfer technique, offers a feasible solution. However, existing distillation frameworks often require manual intervention and struggle to meet such complex user-defined distillation requirements. To bridge this gap, we propose Stratos, an end-to-end LLM distillation pipeline that automates server/model selection, knowledge distillation, and deployment in distributed cloud environments. Given user-defined constraints on model performance and system budget, Stratos automatically selects Pareto-optimal servers, dynamically matches teacher–student pairs, and adapts distillation strategies based on task complexity to optimize cloud hosting. Experiments show that Stratos produces a student model that achieves four times the accuracy of its GPT-4o teacher baseline on a rare, domain-specific Mahjong reasoning task with reverse synthetic data and knowledge injection. Moreover, it achieves reduced latency and cost without compromising accuracy. These results highlight its promise for vertical-domain LLM deployment.