Off-cycle options for Target School Career Switcher

Seeking advice on the next step into Finance, as I have a very hard time believing there are only a few routes to landing a solid role in IB/PE. Long story short, I worked for a few start-ups /family-owned companies after undergrad that had nothing to do with finance. I actually saw a few of these businesses begin to go under as that's when I started getting extremely interested in business models/ cap structures / investing / etc. My next step was to enter into B-school. I simply could not afford a full-time MBA, but I did get into a comparable masters program at NYU STERN (A target school) - by the end ill have an MBA as they allow you to transfer in / choose either the Masters or the MBA since a lot of the courses overlap.

I do not get the benefits of recruitment with the full-time MBA students, and I'm looking to get some experience before I apply to internships on my own. For someone with no experience in finance (although learning a lot from Stern courses,  researching, and practicing financial modeling in my free time), what are some possible options?  Im in hopes to get an off-cycle internship or at least an administrative role in the financial industry to learn some of the ropes and get familiar, and network. Working in the industry even if it's not the exact role I want, will be the most beneficial while working towards my degree.  

Again, I have a few hard time believing you must have had an undergrad in finance, go on to be an analyst, go back for full-time MBA and then move your way up from there. It is so cookie-cutter and I truly think the story starts to sound old after awhile. Clearly, I am taking a very non-traditional approach but I know there are other ways to break into finance without the latter approach mentioned. 

Thoughts?

P.S I live in NYC, my long term goal is PE, but I do realize I may have to start with IB.