Another phone call to the placement office yielded more clarification. If a child was registered by the March 31st deadline, the results of the lottery will be sent out by the end of May. Why it takes 2 months from the close of registration to get results is beyond me. One rumored cause is the number of classrooms at each school had not yet been decided.
The May 28th deadline is an extension for families that missed the March 31st deadline. It is my understanding that these applications will not be processed with those that registered on time. These families will only be able to register for schools in which there are openings. (Some schools will have already met 100% capacity and will be "closed" for registration). In the south zone, the schools that are still "open" for registration include: 2, 3, 4, 16, 19, 29, 35 and 44.
As a side note, given all of the accolades for School 19, I'm shocked that it didn't fill in the first round....