Okay, we'll give it to you straight: none of Booker's plots even comes close to fitting Dead Man Walking. Rags to Riches, the Quest, Voyage and Return… no, nope, nyet. Tragedy, comedy? Neither of those, either. Dead Man Walking doesn't seem like a tricky or complicated book, but if Booker read it, he would drool and lurch and tear his hear out in a fluster of aggrieved confoundment.
Okay, so why doesn't this baby fit any of Booker's plots? Well, there are two reasons. First, the book is about true events. Life, as you may have noticed, doesn't usually have a good, strong, easily defined plot. You don't usually go on a quest and succeed and come back; you go out the door and forget your purse and come back and try again, and then you get where you're going, and you sit down, and nothing happens. And then you have to go somewhere else.
That's kind of what happens here: Prejean sort of goes on a quest, but then she changes her mind as to what the quest is about, and fails, and then sort of goes on another quest, even though she knows that one's not going to work, either. And then she tries to connect with the people hurt by her quest, maybe. There are enough starts and stops and blind alleys to make Booker dizzy.
The other reason that Booker's plot analysis doesn't work is that Dead Man Walking isn't really organized around a plot; it's organized around an argument. The point of the book is not the tragic hero with a fatal flaw. The point of the book is: the death penalty is bad. That's why we get lots of examples and information and anecdotes. They're not there for plot; they're there to prove to that the death penalty is bad. That's just how the book is organized.