I would say no to the MBA.
You have a good GMAT, good GPA, and were able to get an interview at LBS so you are close. You have pretty specific research interests: were you applying to schools that focus on these things? Did you contact professors that are interested in these topics?
UBC/LBS/Toronto/NUS is a pretty diverse range. How much did you tailor your application for each one?
Only thing lacking is research experience. Maybe you should try to apply to something like this: Research Fellows Program | Stanford Graduate School of Business or Pre-Doctoral Research | Programs ... or reach out to professors that do work you do and see if there is a way to collaborate. You didn't mention who your letter writers were, but this will matter if you are targeting the very top programs.
Another option if you really want to start this year is look at HEC Paris: they have multiple rounds of applications so you may be able to get in there, and it is a good program.