Please evaluate for profile for a top MBA (i.e. M7)

Hi Guys,

I'm trying to gauge a sense of my credentials to get into an MBA business schools">M7 school (think WHS). Was hoping anyone with advice on the matter could suggest anything. I've highlighted my background below, however it's a little verbose!

I'm a UK resident (having migrated to London when I was 6 with my parents, as my father was an investment banker), but was born in India. I have been constantly moving between the 2 countries as a child. I was in the UK till I was 16, studying at a top UK public (independent) school, think along the lines of Phillips Exeter etc, where I did well academically.
I then finished my last 2 years of schooling in India (I had to move back due to personal reasons). Didn't do as well as I hoped in my finals, partly due to a lot of the aforementioned personal upheaval and didn't get in to my preferred UK university (think top Engineering college).
I instead went to a Russell Group university, studying Mechanical Engineering (4Y bachelors' course). Didn't bother applying myself for my 1st 2 years of university (in my university, the first 2 years did not count for the degree result) both in an academic and social sense. Into my final 2 years, I gathered my academic mojo back, started doing well. I also got more involved in societies, becoming my university's Finance Society committee member. In the end, I graduated in June 2013 with a First Class degree (highest degree in the UK, think c. 3.7/3.8 GPA)
Career-wise, I've always been interested in M&A in a large MNC bank, especially in the Chemicals sector. This is in part due to my father and stepfather, given that they both are investment bankers and my deep-seated interest in Chemistry as a child. They first took me to their offices as a kid and I remember being thrilled at being at a Bloomberg terminal and figuring out what it was. Before I started working, I had a few internships in the industry, doing a spring internship with Nomura in London, a stint with my father in his boutique M&A advisory firm (in India), in my father's friend's boutique IB (in London) and in a PE firm (in India).
I have been working now for just over 1 year and a few months, with my first job in a large domestic bank in their M&A team, where I was part of a team that closed 2 transactions (1 debt financing and 1 M&A deal with a leading Dutch MNC, in which I led the Info Memorandum preparation and coordinated buyer groups, interacting with the firm's executives). I left that organisation a few months back, since my boss was dissatisfied and left, along with a lot of my team members who followed suit in the months after his departure. But as a gesture of altruism on his part, since my former boss liked my work and me a lot, he put me up to his old boss (ex-partner / chairman of a leading American IB in India) who recently set up his own boutique IB which deals with leading MNCs and corporate houses of India. We are still to close a transaction, however.
At both workplaces, I have taken initiative to develop a lot of the office's utilities, from developing a high quality Powerpoint template to developing financial database templates from scratch for DCF analyses and Comparable Valuation analyses (Bloomberg, FactSet, Thomson Reuters).

Anyhow, I'm wondering as long as I get my high GMAT score (>720) for application to WHS in fall 2016 (I will be 25 in October 2016), how do I sell my story, with what will be by when I apply, just over 2 years of work experience and 1 job switch and lack of brand name firms with full-time work experience?

Any advice would be appreciated. Please PM me if you don't wish to discuss openly in the forum.

Thanks in advance!