I had been assured by the powers that be that 311 and the zone search engine on the DOE's homepage were accurate places to enter your home address and find your zoned school information. It turns out that it is not. Who knew that the DOE's own website would not be connected to their central ATS system?
To find the truly accurate information, call your local Enrollment office between the hours of 8am and 3pm on weekdays or contact the local school that you think is your zoned program to confirm your zone. The school is the place that will be registering you for kindergarten, so you might as well start at the source.
If you live within District 13, 14, 15 or 16 these are the pertinent Office of Enrollment numbers: 347-298-0117, 347-298-0139, 347-298-0160.