Looking to pivot: Should I leave full time job for MBB internship?

Hi! My first post here.

I'm currently working at a healthcare centered VC with 1 YOE while finishing up a masters in finance at a semi-target US university. I don't come from a business background but I've recently taken a career interest in business management. 

I've networked my way into an RA program at BCG's APAC office in the summer. The problem is, I would prefer not to live in the location of the internship long-term, and more importantly it's the only 'internship' program at that office and doesn't provide benefits in getting a full time offer.

A few additional notes about my background: bachelors in statistics (also semi-target), 2 YOE as data analyst(non-finance), lots of NGO work focusing on developing community projects and outreach programs

I am serious about working in consulting, especially if it's in MBB, so I'm considering leaving the job for the internship. Just wanted to hear some advice!

Here are the 3 options:

1) Stay in my current role and apply for a full time role without an internship - basically, does my resume sound too weak to be pivoting without consulting experience?

2) Quit my job, go for the 'internship' in the summer, and hope I land a full time job in consulting after finishing my masters - How do you think foreign offices would consider the experience?

3) Should I try to look for other internships that gives a better chance to land a full time offer afterwards?