Entering 3-year Masters in Management - Seeking internship advice

Hi all, I will be commencing a Masters in Management at a top European business school this fall (think IE, ESADE, HEC tier). For those unfamiliar with the MiM program, it is a 3 year degree where the 2nd year is reserved for placements (ranging 3-6months each). For various reasons, I want to break into BB IBD post-Masters and am looking to fully utilise any spring weeks and my 2nd year for internships.

Just to clarify my starting point - I'm switching career fields and am totally new to this game. My undergrad degree is non-quantitative (think History, Politics, etc) and from a semi-reputable UK university; my previous internships have all been non-quantitative as well, although they have involved corporate work (envisioned a very different career before this.) Effectively I'm starting from ground zero, but I fully understand it's an uphill battle and am willing to work double / triple / quadruple overtime to catch up.

So, rock bottom beginnings aside, this is what I will have starting this fall: GMAT 770, First Class Honours at undergrad, CFA Level 1, an intensive one-month summer program at one of the M7 US business schools, and a scholarship from my Masters school. I am also aiming to complete a few financial modelling courses this summer, such as WSP. Unfortunately I think my undergrad degree and previous internships can be fully discounted here.

My tentative plan for Years 1/2:
Year 1 Spring - Couple of spring weeks in London (common for MiM students)
Year 1 Summer - ???? (aiming directly for BB IBD internship, but don't know if this is realistic.)
Year 2 Fall / Winter - Off-cycle, 6-month Banking / Consulting internship
Year 2 Spring - Might try to mix a PE / Consulting internship in here.
Year 2 Summer - BB IBD internship.

Ideally, (obviously a massive long-shot here) I'd like to finish my degree with one BB IBD internship, one PE internship, and one MBB consulting internship, to build up my skillset and exposure to different industries. What I'm unsure about is what "range" of firms I should shoot for during my 1st year summer: should I go directly for the BB banks or is that just out of my league? Should I structure my internship timeline for consulting --> banking or banking --> consulting?

Many thanks and would deeply appreciate any advice. General comments on my tentative timeline would be welcome as well.