If hands-on experience is what you're most interested in, then I do think an MSW (or dual MSW/MBA) program makes more sense for you. An MBA program at a very non-profit-oriented school (such as Yale or Haas) will give you great training, but it will definitely be more theoretical than hands-on. Depending on the school, you will probably be able to get involved in at least one class/project with meaningful hands-on experience, but that will be a relatively small drop in the bucket compared to most of the learning, which will take place mostly in the classroom. Beyond those opportunities, at a traditional business school you may need to go make your own opportunities (which isn't out of the question).
Re: financial aid, you could try to hook up with a more significant organization that may ultimately be willing to sponsor you after you spend a couple of years at the organization. They sometimes have partnerships with good schools where the NGO sponsors you, and the school essentially gives them a heavily discounted (or even free) price. Alternately, I don't know a ton about them, but I know there are federal grant opportunities for students who are interested in studying social work and devoting their careers to that line of work. There are also a lot of loan forgiveness programs in this area, too, although they sometimes have pretty strict requirements.
I hope that helps!
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