A 28-year-old man with a history of poorly controlled type 1 diabetes mellitus presents with a 2-week history of progressive fatigue and weight loss. He admits to poor medication adherence and has been consuming a high-protein diet in an attempt to 'build muscle.' Laboratory findings: blood glucose 320 mg/dL, arterial pH 7.22, HCO₃⁻ 10 mEq/L, serum ketones strongly positive, blood urea nitrogen 32 mg/dL, and creatinine 1.4 mg/dL. Serum amino acid levels are markedly elevated. Which of the following best explains why gluconeogenesis from amino acids is paradoxically INCREASED in this patient despite severe hyperglycemia?