Hi,
I definitely don't have enough knowledge about various schools to answer your question in its entirety, but I just wanted to give you my two cents regarding Hunter, where I am currently a student. The student body at Hunter is extremely diverse and there is a really wide variety of educational backgrounds, work experience, volunteer experience, etc. There are people there (myself included) who had very little experience (paid or volunteer) in social service. Some people are quite young, some are older and looking at a second (or third career). I guess my point is that based on what you've said about yourself I don't see a reason why you couldn't get in. I definitely don't think it would be "overshooting".
I will mention that when you apply to Hunter you have to declare a track, so you would have to choose between clinical, community organizing or organizational leadership. You are required to take both clinical and policy classes, however, and you have a couple of electives so you can take classes that cover different areas despite being committed to one track.
Hope this helps in some way.