Anything is always possible, but a 560 score as you are aware, will make an MBA program pretty difficult. You could perhaps look at programs like University of Pittsburgh or other programs in that tier. I think your professional experience is interesting and it seems that you have consistently been a top performer, but I'd say your background is a bit nontraditional as far as MBA goes. That doesn't mean that you can't get in, but you'd likely have to aim for lower tiered programs. I'm not as familiar with Masters of Finance requirements, but I imagine that similarly, you'd have to look at lower tier schools.
Best of luck,
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