One-year MBA program in my case

Hi everybody, I posted something on the forum back in July, but after going through some job applications, I had to refine my thoughts, so, therefore posting another topic.

I am a South Korean citizen, and I have worked in corporate banking for 4 years at a well-respected bank there. I moved to Europe a year ago, now working at a European bank (think CS, UBS, DB) in credit risk management.

I have seen many of my colleagues from my former bank going to top schools, and since my current bank is a bulge bracket bank, I think I have some shot at getting admitted to top schools if I get a decent gmat score. I was initially thinking of applying to a one-year MBA program at Insead or LBS's MiF program with an intention of landing a job in London, but my past several months of experience of applying to positions in London convinces me that I might not be able to successfully break into a job there even after I get a degree from Insead or LBS (I only have an undergraduate degree from South Korea). I've been applying to credit analyst roles and rating agencies, and while most of them rejected me, I have been able to receive several contacts from HR departments and headhunters from London. But, not surprisingly, they turned me down because I had to receive a sponsorship from the applied firms. All of this wonders me if the situation would change even after I get a degree from these two schools.

I have done some research afterwards, and I've figured out that maybe a U.S. MBA degree might be more of a door opener for me in terms of getting a job in NYC upon graduation compared to the London path. The impression I took away after applying to London was that it is not that very open to non-EU citizens. And compared to that, the U.S. at least gives a 50% chance of getting a Visa after going through a lottery process. After figuring this out, I narrowed down my choice of schools to three schools: Kellogg, Johnson, and Marshall. All of these schools have a one-year accelerated program, which makes more sense in my current situation considering my current age (just turned 31) and my saved-up money. After graduation, I want to work in leveraged finance or other credit-related front office roles.

The biggest catch is that I won't be able to have a summer internship by attending these programs, and I believe this can considerably hurt my full-time prospects, especially given that I am trying to make a career switch (corporate banking/credit risk to FO) and I am a non-US citizen.

What do you guys think? Given my current situation, would I have a shot at getting a full-time offer if I complete one of the one-year programs at these schools?