If you're delaying the post then you don't need to add chapters to hide your school.
And yes saying your class status and major can identify you unless everyone at your school who is rushing is a senior engineering major for example. Unless you're an incoming freshman giving your status and major is pretty obvious, and it only takes a few more pieces of information for people to track you back from there.
As for honesty, go for it. You seem to have thought the whole thing through pretty well so you're probably in a good place. In the end though, remember your recruitment's about you and not about how to write a story for us
