Is MSF a legitimate way to rebrand and network into banking?

So I figured out about half way through my undergrad degree that I want to end up with a career in Finance. 

I'm a 3rd year undergrad, non-target but decent private school, formerly a Math major, now a Finance/Math student, 3.7~ GPA, I have quite a few electives in computer science, statistics, and upper division math courses. Decent extracurricular involvement in some finance/entrepreneurship clubs. I transferred schools so it'll take me one extra semester to graduate, which is good in a way since I have two summers to intern now.

I'm fortunate thanks to personal connections I'll be able to get an internship or two before I graduate in Finance at F500 companies at the very least, and hopefully I can leverage one of these to get a banking  internship. 

I'm really ready to dedicate myself to studying my butt off and for the GRE/GMAT and trying to go for a top program. I want to end up in a front office role in a big bank (so does everyone), but I know given my experience/credentials at the moment this isn't really possible, so I want to use the MSF to rebrand, specialize, and network hard.

I've already started networking with alumni hard at my current university, scheduling calls, coffee, cold calling for middle market type positions (I got a few interviews, but it seems like my lack of the experience at the moment is where I'm behind).

I've read up on Vanderbilt, Villanova, and Georgetown so far, what other schools should I have on my radar (MSF not MSFE)?

Is this a good/legitimate plan for me to pursue to break into a solid financial career? 

Thank you