Double Degree HEC MiM or Exchange at Columbia/LBS/... and Internships

My issue is very specific, but perhaps one or two of you might have some good thoughts for me...

I am a MiF student at a continental European target school (St.Gallen/Bocconi/ESADE) and have two options on how to continue my studies. My ultimate goal is to get into UMM / MF PE, which is probably the easiest via an analyst stint at a BB - so that's the medium-term goal. I basically want to know which option would maximize my chances and is more career-enhancing.

(My degree takes 1.5y which is important for the context.)

• Double Degree at HEC: MiM with a specialization in International Finance (similar but not equal to their MiF). Would essentially cost me 6 months as I would spend 1y at HEC and only 1y (instead of 1.5y) at my current University. I'd get two post-grad degrees.
• Exchange at a top-notch university such as Columbia or LBS: Wouldn't cost me any time as I basically would spend 6 months of my 1.5y degree abroad. This would mean, that I could spend 6 months on internships which could help me land a desired role.

I am leaning towards the exchange as I understand the value of internships. Yet, I'd definitely prefer the Double Degree.

What would you recommend?

Background: I did my BA/BSc at the same University I'm at now, and did an exchange at a British school (Oxford/Cambridge/LSE). Internship-wise, I've got MBB, upper MM IB (HL/Jef/Laz) and IB at a local bank.