Dramatica is an excellent tool for constructing and writing a debate and other forms of persuasive discourse. Since the theory is based on the concept that stories exist because of inequities, and a specific story is a specific "argument" (or Grand Argument Story as we call it in Dramatica) that an author makes to his audience, it naturally follows that the same form and techniques can be used in most any positional form of writing. How would one use it? Hmmm. I suppose there are a number of ways to do that. Here's how I would go about doing it:

1. Identify the central inequity around which the debate or essay is centered.
2. Determine your position on the inequity.
3. Create a storyform that best resembles the argument you want to make taking particular note of Story Outcome, Story Judgment, MC Resolve, and Story Limit. Though you can explore and emphasize any of the dynamics, these seem to be the common points of reference in a debate-style argument.
4. Determine the throughline you see as most important to your argument. Though you will want to make the entire argument from all four perspectives (if your idea is to make a bullet proof argument), it's still a good idea that you have a sense of which is a "more appropriate" point of view for the argument you make.
5. Instead of characters, treat the character elements as topics of discussion. Use the Variations to make "thematic" commentary. Use the Types to organize the flow of the argument. Use the Domains to show the valid perspectives (points of reference) that frame your argument.

I think these would give you a good headstart on any type of persuasive writing you might like to do.