Nonprofit to IB

While I was studying finance at the University of Nebraska, I assumed that I would be entering into ordained ministry for my church and did not pursue internship experience. After spending a year in a nonprofit missionary organization on a university campus in New York following graduation, I have changed course away from ministry (various reasons, many of them personal in nature) towards investment banking. As I am concluding my second year (the program is a two-year commitment), I am beginning to apply for analyst jobs here in the city, but my lack of experience and nontraditional career path has been challenging.

I have received conflicting advice for my current position (apply to FT roles anyways, apply to internships instead, or apply to MBA programs). For internships, most applications make it clear that only current students are eligible. Has anyone else faced a similar struggle in some form, and is there advice you would recommend?