Dear New York MBA Guy,
I will do my best to answer your questions. However, MBA admissions is not as exact a science as many would believe and so there is no formula you can plug your profile into in order to calculate your chances at a school. Applicant pools do change year-to-year and schools have goals every year of what they want their incoming class to "look" like. Without knowing these goals or the make up of the applicant pool, I really cannot give you percentages but can only comment on your whether or not I think you have the foundation for a competitive application.
Based on the amount of information provided, I do think you are a competitive candidate for any MBA program. What will make the difference is how well you position yourself and put together your application. What you list as potential weaknesses are not really weaknesses, per se, in your application. Schools do not want their MBA classes to be made up of mainly consultants and bankers; they want a diverse group of people in terms of work experience, education, and life experiences.
The main concern (really question) the admissions committees will have for you is why do you want the MBA after you just finished the MPA and how does that make sense for your future career goals. Likewise, why do you need your MBA to work in healthcare administration and how does this particular program make sense for this career path? If you can effectively convey a solid rationale for doing your MBA, then you will be in the best position to get into at least one of your target schools.
Finally, it would behoove you to start making some personal connections with admissions folks at your target schools. Obviously, you do not want to email/call/visit too much, but you want them to associate your application with a person. Take advantage of any opportunity to interact with representatives and absolutely set up a campus visit this fall to attend class, tour the school, and talk to students. Likewise, it can't hurt to find some alumni from these schools to connect with that might email the school an endorsement of you.
Best of luck,
Lisa