A 38-year-old woman with a 4-year history of seropositive RA (RF 220 IU/mL, anti-CCP 110 U/mL) well-controlled on methotrexate 15 mg weekly presents with a 3-week history of progressive dyspnea on exertion and a dry cough. She denies fever or chest pain. Chest X-ray shows bilateral interstitial infiltrates. High-resolution CT chest confirms usual interstitial pneumonia (UIP) pattern. PFTs show FVC 65% predicted, DLCO 48% predicted. What is the most likely diagnosis and the most appropriate next step in management?