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Since your goal is a top-10 US program, you might as well go to Columbia now. I doubt that their MAO program is better than LSE's PhD program (first year) in terms of educational quality, but you'll be leaving after a year anyway, and faculty members might be more willing to write a recommendation letter for a Master's student going on PhD rather than a PhD student transferring to another PhD program. I don't imagine that getting into Columbia's PhD program from their MAO program would be too hard either, although I could be wrong.
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