Your proposed subject is still pretty broad for an undergraduate
thesis--you'd need the scope of a dissertation or a book to do it justice.
However, you mentioned:
"I want to look at how they impact the narrative "distance" between Twain,
the first-person "I" that often introduces the stories (if they are
framed), and the character actually relating the events."
Maybe just take a few of the stories and examine the relationship between
Clemens, Mark Twain, the narrator, and character telling the stories. The
frog, the old ram, the blue jay yarn, Huck's relating of the balloon
voyage, the True Story, and the snow-shovellers all come to mind.
Ron Powers's biography of Clemens (Mark Twain, A Life. Free Press: New
York, 2005) has some insightful passages about how Clemens framed his
stories in relationship to his predecessors in American humor such as
George Washington Harris, Joel Chandler Harris, and "Artemus Ward."
Disclosure: Powers dedicated his book to Bob Hirst, editor of the Mark
Twain Papers, so here at UC Berkeley, well....