Recent large language models are increasingly being adapted for medical reasoning, yet most open medical LLMs remain optimized for English-centric clinical settings and fail to capture local legal and institutional knowledge. We present Meerkat2, a family of open medical reasoning models at 14B, 32B, and 30B-A3B scales for Korean and English clinical contexts. Meerkat2 is trained on an 837K-example mixture that separates reasoning transfer from high-fidelity local knowledge: clinical reasoning is distilled from strong teachers, while Korean medical statutes are converted into source-grounded question-answer pairs. We also introduce Verbosity-Decoupled Distillation (VDD), which preserves the benefits of long teacher rationales without making verbose generation to the student’s default behavior. Across MedQA and KorMedMCQA, Meerkat2 substantially improves over comparable base models, with the 30B-A3B variant reaching Korean licensing accuracy that matches Qwen3-235B-A22B while using only 3B active parameters. Ablations show that statute-grounded synthesis outperforms standard distillation, and mechanistic analysis reveals that VDD cancels gradients toward verbose generation. These results provide a practical recipe for localized and efficient medical LLMs.