Slice the tops from the peppers, remove the seeds and stand the peppers in a greased 6-quart slow cooker.
Combine the rice and water in a saucepan, bring to a boil, cover and cook over low heat until tender, 15 to 18 minutes.
Heat the oil in a skillet and brown the turkey with the onion until no pink remains, 7 minutes; add the garlic for 30 seconds.
Mix the turkey, cooked rice, 3/4 cup tomato sauce, oregano, salt, pepper and 1 cup mozzarella.
Fill the peppers loosely, spoon the remaining tomato sauce over their tops and add 1/2 cup water to the bottom of the cooker.
Cover and cook on low until the peppers are tender and the filling reaches 165°F, 3 1/2 to 4 hours.
Top with the remaining mozzarella, cover for 10 minutes to melt and lift the peppers out with a wide spoon.