Welcome again to the teaching profession! Out of curiosity - did all of your advance reading help you put together a good presentation? What did you wind up doing for your lesson?
I think PS 262 sounds like a good choice. The fact that they wanted to see a demo lesson PRIOR to offering you a job suggests that they're not just looking for warm bodies to fill vacant slots. I am sorry to say that given the shortage of teachers throughout parts of the United States, this is precisely what some school districts do. They plug people into slots and hope that things will work out.
The fellowship idea being implemented by New York seems to be a more sensible approach to finding good people to fill vacant slots. Assuming the program has lots of built in support - there should be less overall problems for new teachers.
I hope you'll continue to visit us.
I would enjoy hearing stories about your experiences.
P.S. Which grade will you be teaching? Will this be a self-contained class?