First off, the idea of constructing your final paper as a narrative, and one that is highly self-aware in terms of the topic ("Why I Deserve to Pass This Class") is a very good one. Like your teacher, I implore you to do so without patronizing, by which I mean without condescension of the offending kind. But in order to be most effective in that, start your essay with a bang: by being offensive and condescending. I'll explain.
So here I am sitting at the computer trying to figure out what exactly I am going to write to indeed coherse you into passing this paper and in return allowing me to pass the class.
For this being merely part of your free writing, this is a good start: I am going to coerce you into passing this paper.
However, for this to work, you have to lay on thick layers of irony and self-awareness. After all, you state outright that you thought you could sleepwalk through this class. So I suggest that you incorporate that swagger into the beginning portion.
In the end, however, you are also on the right track with your realization of what the class is truly about. Sure, you read some books, you delved into some esoteric areas that are about as foreign now as they ever were. (Hamlet
, for example.) But, if I understand correctly, it's the set of standards you were held to in order to succeed that have stuck with you the most.
With a healthy dose of deadpan humor -- in other words, using haughty patronization as a smokescreen, if you will -- you can make this work. Expand and philosophize a bit on your experience of coming into this class with preconceived notions, only to have them altered for the better.