A 42-year-old woman with severe asthma is undergoing emergency appendicectomy under general anesthesia. Five minutes after induction with thiopental and intubation, the SpO₂ drops from 98% to 82%, peak airway pressure rises to 45 cm H₂O, and the patient develops diffuse wheezing. Blood pressure remains 110/70 mmHg. What is the most appropriate immediate next step?