Career Advice: P/E, CA/CFA, More school

Looking at several career paths with the goal of breaking into a BB investment bank.

Background: Non-target, 3.8/4.0 gpa - Finance.
As a student athlete I spent my summers training and therefore had trouble gaining the work experience needed to gain sufficient networking and industry exposure. I have several interviews with prestigious banks due to networking, however, I am weighing contingent plans and would like some input!

I have an internship with a big 4 CA firm this summer. My goal is to complete my CFA in line with my CA. While working at the firm, I want to move into corporate finance and specifically M&A transactions as it is the most relevant to IB. After this, perhaps, apply for a top 10 MBA program to break into IB if I haven't been able to do so already.

My next option is to work at a 250m PE firm (Distressed real estate - focusing on NPL/REO 1st lien mortgages) . Obviously this is more related to IB, however, isn't the firm a little small? And in addition to this its not an international firm - seems a little less opportunistic.

Lastly, im looking at triple majoring (finance, accounting, economics). This would take another year of school, and could open more opportunities for applying as an analyst. In addition I would continue to pursue a CFA.