Dear amedm,
I think you have a shot at both Columbia and Cornell with the profile you posted. The key will be how well you present your background and experiences in your application. Depending on what your undergraduate degree is in and how many business courses you took, there could be other accelerated programs that might be a fit. However, most US schools that offer accelerated programs specify that you either have an undergraduate degree in a business discipline or a certain number of hours/specific courses in business to qualify. I think you have done a thorough assessment of your profile and the schools; you are correct that you can receive a top-notch general management MBA from both Columbia and Cornell. LBS could also be a strong candidate for you, so it would be worth your time to research the program and see if the curriculum is what you are looking for in your degree program.
Best of luck,
Lisa