I've taken the meatiest paragraph to unpack. The more I examine your statement, the more it becomes clear that there are major gaps in your understanding and application of deconstructivism. I suggest you re-read foundational deconstructivist theory, as I'm not convinced it's the approach you want to take.
"To facilitate better communication and understanding of people with strikingly different experiences I will first use Deconstruction to break down axiomatic views of other groups so they can be replaced with more inclusive ways of discussing our experiences. Deconstructivism has nothing to do with facilitating "better communication and understanding of people," but rather approaches literary texts in order to note tensions and contradictions within a (perceived) unified text. It demonstrates that meanings are multiple and unstable and points out where 'slippage' occurs.
I will do this through the use of American Modernist writers and their fascination with internal thought processes and the exceptional variance within every human life. Authors that I am interested in include: Sherwood Anderson, Gertrude Stein, Hemingway, and Faulkner. I take this to mean you have authors whose work you'd like to 'deconstruct.' Yet deconstructivism has been around since the 1970s; surely this has already been done. Drop what you're doing and go read how scholars have deconstructed particular works so that you can participate in this conversation. You need to know what others have done in order to make a convincing case as to what you'll contribute.
These authors pushed for something new in their writing and this extends to how they represent thought. This is not very clear. What is new about their writing and thinking? And how does deconstructivism apply? This highlights the differences in not just what we think but also what leads someone to having that thought. I don't understand this sentence. This time period and group of writers is an important resource for those trying to build relationships and strengthen communication." Are you saying that modernist texts offer insight into human relationships and behavior? If so, what insight? And how does deconstructivism help us understand that?
Stepping away from your statement, can you give me your elevator pitch? What is it that you hope to learn, and why is it urgent and important?