Ms. R,
At the moment, your child/children can keep going to School 12 even if you move to - not only a different neighborhood, but out of the zone as well - so basically, anywhere in the city. (I'm NOT sure if siblings who aren't in the school yet would be able to go if you moved out of the South zone.)
If the school board stays in control, I don't see that changing significantly - even if there were a move to encourage people to attend their neighborhood schools, there is a strong commitment to choice as well.
I don't know what the mayor's vision of neighborhood schools is. I would very much like to know! But as someone who has been involved in the school choice/neighborhood schools question for many years now, I can tell you I would fight hard to make sure no child was "required" to go to their neighborhood school (and I say that as a proponent of neighborhood schools!)
Honestly, I can't see your child being forced to switch schools, no matter who's in charge. I think everyone appreciates the value of children being able to continue in the same school. (Originally the school choice plan wasn't supposed to let people stay in their schools if they moved out of the ZONE (not the neighborhood) but people just move too much, so everyone has been allowed to stay at their school no matter what - one reason busing costs are so high, and why the zones are so meaningless, except as an instrument of torture for incoming kindergarten parents!
I know I am rambling without having much real information, but I don't think you should move out of the city over this! (And what a terrible irony that would be - when Duffy's whole goal is to keep families IN the city!!!)
I will see if I can find anyone more knowledgeable to tell you more ...