T & N & Z are all indepedent of each other. T fares are only available on the eastern triangle/maritimes route. N class is the lowest published fare AC sells while Z is consolidator fare such as the Student Cuts ticket that you're buying. The most important thing is "Z" doesn't earn any Q miles.

One question - Do you have to go via YUL? If not, there are plenty of options via YYZ at a later time.

There are later LGA-YUL flights departing on Aug 31 but maybe Z class was all sold out that's why your TA told you that's the latest flight you can get in Z class.