Completely change course and get an MSEE?

[caviar]

I'm a senior in college studying finance, and everything I've done so far has been in preparation for a career on Wall Street. I've interned investment banks (Goldman Sachs, Morgan Stanley, etc.) and private equity firms, and have a very prestigious full time job offer for after graduation.

But I'm starting to have second thoughts about working in finance. Is it too late to turn around and go into engineering? I could take an extra year and get a second bachelor's in EE (I've taken some introductory engineering classes so it would be doable). Could I then apply for a Master's in EE next December?

I've never done research/internships or anything outside of class remotely related to engineering (everything I've done has been finance related), so I was thinking about doing some research this summer and taking an extra year for the EE degree+do more research+take GRE+get letters of rec.

My question is how will an MSEE admissions committee look at the application of someone who has done nothing but finance for the past three years? Will the lack of research significantly damage my chances at a top program? What would be the best way to spin my story?