You're not working any system. While NYU may accept applications earlier than most schools, since they're not part of VSAS, it won't be processed until they have finished scheduling all of their own students (which isn't until May). Visiting students are allowed to register for whatever spots remain. They'll probably lose an application that is sent in 12 months before scheduling begins.
In any case, it's not difficult to schedule electives in June since most schools are still finishing up their academic year. July and August are considerably more difficult.