Research careers other than professor?
Several people I know who studied public health have gone onto research careers at universities that have affiliations with hospitals. They are considered faculty members, but they have no teaching responsibilities. Besides research, they are expected to contribute to submitting research grants for their respective units/departments. Some are more independent than others, with one person essentially having the responsibilities of a senior postdoc, while another runs her own group within the hospital itself. For example, this unit may represent what you're looking for (I am in no way affiliated with them, and just came across this via Google).