Claremont McKenna BA + BS with Columbia/Cornell/other Ivys

I'm currently in the thick of college applications, and I've already set my sights on Wharton for the early decision which I've already applied to, but I've been doing a lot of research on CMC and absolutely love the academic programs there and the idea of the college as a whole is very appealing (strong Political Sciences/Philosophy/Economics departments, good mix of liberal arts and humanities with professionally driven kids) but I am still hell-bent on getting an investment banking job out of undergrad in NYC just for the sake of experience. I saw CMC's BA+BS program often pairs with Columbia or Cornell where you get a BA in Econ from CMC in 3 years and a BS in an engineering program in 2 years which seems like a pretty sweet deal on paper even though it'll be a lot of work.

My high school has good ties with CMC and we always send 3-4 kids every year from our class size of ~160. My STEM side is very strong but I find it rather boring at high school at least, although maybe Columbia could change this with a Financial Engineering BS or something. I was just wondering how this profile would look to recruiters (i'd assume pretty amazing but idk maybe it'll make me look like an indecisive stretched thin nerd) and whether y'all would advise it. I suppose my 3 years at CMC will be rather fun and my 2 years at Columbia/other ivy would be more professionally and technically driven. I also have also considered a 5-year MA in econ from CMC or just regular undergrad there and an MBA down the line, but I'm almost 100% sure if I ED II there, I'm guaranteed to get in. 

Any thoughts will help, thanks!