A 45-year-old female accountant presents to the emergency department with a 3-hour history of sudden-onset, agonizing upper abdominal pain. She describes a long-standing history, spanning several months, of a "burning" sensation in her epigastrium that typically occurred about 2-3 hours after meals, was often relieved by antacids or eating a small snack, and occasionally woke her from sleep. She attributes these symptoms to stress from her demanding job. However, today, after a light lunch, she experienced an abrupt, severe pain that rapidly spread across her entire abdomen and was not alleviated by her usual antacids. She denies any recent trauma, but she has noticed dark stools intermittently over the past few weeks. On arrival, her blood pressure is 110/70 mm Hg, pulse is 98/min, respiratory rate is 22/min, and temperature is 37.8°C (100.0°F). Physical examination reveals a distressed patient lying still on the stretcher, with shallow breathing. Her abdomen is exquisitely tender to palpation, rigid and board-like, with generalized guarding and rebound tenderness, particularly in the epigastric region. Bowel sounds are absent. Rectal examination confirms dark, guaiac-positive stool. Given this clinical presentation, what is the most appropriate immediate diagnostic imaging to confirm the suspected diagnosis, and what is the definitive management strategy?