Alternate Dicourses - I'm not sure how to tell my students it's OKAY

Sorry I took the deadline for this post down to the wire... Lost track of time. This is first class I've taken in graduate school to attempt to explain to me the overall use of alternate discourses in academia. While I'd been exposed to the idea before, but I'd never tried to convey it to someone else, as a teacher does for a student.
When I tried to explain something like different types of literacies to my first-year-comp students, they looked at me like I was crazy. Because I couldn't find a way to even explain the definition of the alternate discourse concept, I could not find a way to incorporate it into my teaching style. They've been exposed to the traditional model for so long, that Bizzell's idea of different discourses in the teaching of writing/composition is alien to them, and to be honest, not a little alien to me as well.
She (Bizzell) sees traditional academic discourse as a way of promoting hegemony in the classroom. If traditional methods use language that comforts white, male, middle class students, she encourages us to challenge our students into stepping outside their boundaries. (Hybrid 11)
After she quoted Dr. Villanueva, I automatically thought of something Dr. Eddy spoke on when he described alternated forms of the English language and how putting slang, other languages, and personal narrative, etc. into academic texts was a form of hybrid discourse.
I do have to agree with Bizzell's thoughts on eeveloping a curriculum that uses alternative/ hybrid discourses, but wasn't sure how to go about that in the FYC classroom. The majority of the students I'm teaching are fresh out of the high school English classroom. Maybe they took AP or Honors English but the University comp program is still unfamiliar to them.
In reading Bizzell's "Basic Writing" I couldn't help but think about how many papers I have read in the Writing Center over the last 3.5 years. Students come in every day with assignments insisting they have to write it the professor's way or their grade suffers. My job at the writing center as a tutor is to help them do that in the most efficient/painless way possible. Most professor's in other fields aren't (in my experience) open to alternative discourses in the classroom. Traditional is the least "messy." If I could tell just one student to step across that traditional/ alternative discourse line, I wonder what they would come up with?
As a teacher I have to try to find a way to teach students what they need to know to survive their other college writing, but expand their idea of discourse/ literacy beyond what they know. By allowing them to keep their writing style, I think they can create a new niche for themselves in academia. We have certain standards for how we critique college writing and they'll have to live up to that, but it doesn't mean they have to lose their voices.