Place pork roast in slow cooker and fill half full with water. Cook 4 hours on high.
Drain water from slow cooker and cut pork into thirds.
Mix salsa, Dr. Pepper, and brown sugar together in a bowl. Pour on top of pork and cook for 4 more hours in the slow cooker on low.
Drain liquid and shred pork. Save some liquid and mix it back in with the pork to keep it moist.
Preheat oven to 350 degrees F.
Evenly divide pork, refried beans and cheese between 8 tortillas.
Fold up each tortilla into a rectangular packet around the filling and place folded side down in a 9 x 13 inch baking dish.
Spray the tops of the chimichangas generously with nonstick cooking spray (you could also use a pastry brush and lightly brush the tops with olive oil).
Place in preheated oven and bake for 15 minutes.
Remove from oven, turn over each chimichanga and return to the oven to cook for an additional 15 minutes.
Top with sour cream and avocado before serving.