A 28-year-old man with a known history of Hashimoto's thyroiditis is being evaluated for persistent symptoms despite levothyroxine replacement. His TSH is 2.1 mIU/L (normal: 0.4–4.0) and FT4 is 12 pg/mL (normal: 9–17). He complains of fatigue and poor concentration. Which investigation is most appropriate to assess his thyroid hormone metabolism and peripheral conversion?