How to move into a good school zone

We are not in a good school zone (probably why our rent is cheap). But we are near PS199. I understand that the UWS PS199/PS87 may be (/are?) going lottery. I'm willing to move, but I hate thinking of moving, paying more rent and still not getting in to public. This is one of the reasons we've been sitting on the fence to buy. I can afford more housing cost OR private school, certainly not both. I've heard some people who rent a second apt, ala cheap studio, in the school zone to see if they can get in. Any advice? Staying on the UWS is my preference but we will move to UES, Brooklyn, heck, Charlotte if we can get jobs. Thanks in advance.