Breaking in from a non-MBA master's degree?

Looking to get some opinion's on breaking into consulting from a non-MBA master's degree. I graduated last May from a nontarget school with a 3.89 GPA as a finance major. I'm currently working at a F100 biotech company on the FP&A team. I know this is the industry I want to work in (healthcare in general, not necessarily just biotech) but this type of work is extremely boring to me.

I've been looking into master's programs, specifically Carnegie Mellon's MS Healthcare Policy & Management. The program has a lot of data analysis / analytics / finance built into it which makes it look fairly interesting, but it obviously focuses on healthcare. Another thing I like is it has an internship built in like an MBA.

It's a small program, but apparently 7-8 out of the ~20 people go into consulting while another 10 or so go into the general healthcare industry. If I went into it I'd be aiming for Big 4 or McKinsey as they're really the only firms with offices in the city I want to be in.

Thoughts?

Edit: I figured with two years of finance experience (by the time I matriculate) in a large biotech, and then a specialized healthcare master's that'd be a pretty strong background for healthcare consulting. Not sure how accurate that is however.