A 42-year-old man with a 10-year history of poorly controlled type 2 diabetes mellitus presents to the emergency department with a 4-day history of progressive fatigue, nausea, and mild dyspnea. He admits to poor medication adherence and has been on a very low-carbohydrate diet for weight loss. Vital signs: HR 98/min, RR 22/min, BP 128/82 mmHg. Laboratory findings: blood glucose 380 mg/dL, pH 7.22, HCO₃⁻ 14 mEq/L, serum β-hydroxybutyrate 6.8 mmol/L (normal <0.6), serum osmolality 315 mOsm/kg. Which organ is responsible for the majority of ketone body synthesis in this patient, and what is the primary substrate being utilized?