A series like that of the SCE ebooks, where you had a small team of medical experts sent in to deal with particularly hazardous missions might work. You could have longer arcs dealing with bigger issues as well as stand alone episodes for one off issues. So long as they had the right characters, with the right dynamics, that played off well against one another then it could work--most people don't watch medical dramas to learn about diseases or the human body, they tune in because of the main/supporting cast that they're invested in.
The focus could be on a specialist team, with the ships crew being more in a supporting role. Like the SCE team, a small, fast, versatile ship would make the most sense, they can get to a crisis quickly, make initial assessments and call in reinforcements as needed without risking a lot of personnel.