Career Advice: Breaking into GS with an Accounting Background

For most of college I thought I wanted to do accounting as a career. Only had a change of heart recently and got really into finance, now I think my dream job would be working at a hedge fund or a similar business managing investments. I go to school at a non-target, but I learned that some executives and other employees at a specific GS office are alumni. As a result a good chunk of new analysts are actually hired and recruited from my school every year. Ideally I'd like to get an analyst position either in equity research or investment banking to build up that experience needed for breaking into the hedge fund industry.

I have a good GPA (3.85) and a strong accounting resume but I'm not sure it will be enough to get an interview for these positions. Since I only recently became interested in finance, I don't have much finance-related work experience, coursework, or involvement to put on my resume. 

One potential foot in the door I've considered is applying for a controller position. I think I have a much better chance at getting an interview given my strong accounting background and resume (Internship at Big 4, placed in an accounting case competition, 4.0 in all accounting classes). I'm not really interested in working in controllers long-term and would prefer to work in the divisions mentioned above, how likely/easy is it to transfer divisions if I were to get hired? And if switching divisions is not a possibility, would a career in controllers do anything to help break into a hedge fund?