Bring mirlitons and water to cover to a boil in a Dutch oven; boil 45 to 50 minutes. Drain and cool. Cut in half lengthwise; remove seeds, and discard. Scoop out pulp, leaving 1/2-inch-thick shells; chop pulp, and set shells aside.
Sauté onions and garlic in hot bacon drippings 5 minutes. Add shrimp and ham; cook, stirring constantly, 3 to 5 minutes or until shrimp turn pink. Stir in mirliton pulp, 1/2 cup breadcrumbs, and Creole seasoning; cook, stirring occasionally, 5 minutes. Stuff mixture evenly into mirliton shells.
Sprinkle with remaining 1/4 cup breadcrumbs and cheese. Place in a lightly greased 13- x 9-inch baking dish.