Not the way to find a crashpad
The Gaeta Group 718-441-1144
Since you asked for it, here's their number. I am typing this as I sit in one of their units. They manage one complex refered to as the "Townhouses" near Lefferts and Metropolitan at the heart of "crashpad central." They may have other properties, but I am unaware of them.
Today might be a bad day to ask me about them, since we have about an inch of water on the floor from last night's storm. Overall, these are not bad units--by NY standards!
So here's the kicker... If you have 10 or so people who want a crashpad and have somebody who manage it for you, give them a call. They might be able to find you a unit. They do not deal with individual placements into their apartments.
The best way to find out what individual slots are available is through flyers posted in crew rooms at the companies that fly out of the JFK/LGA area. Julie was on the right track to ask people if they know of any specific vacancies.