Whisk together the honey, chili powder, lime juice, and minced garlic in a large glass or ceramic bowl. Add the shredded cooked chicken and toss to evenly coat. Cover the bowl with plastic wrap, and marinate in the refrigerator for at least a half hour. Remove the shredded chicken from the marinade, and shake off excess. Save the used marinade.
Preheat an oven to 350 degrees F (175 degrees C). Lightly grease a 9x13 inch baking dish, and spread 1/2 cup of enchilada sauce over the bottom.
Combine marinated shredded chicken with 5 cups of shredded Monterey Jack cheese in a bowl. Mix lightly. Spoon about 3/4 cup of the chicken-cheese mixture down the center of each tortilla. Roll tortillas and place seam-side down in the prepared baking dish.
In a bowl, whisk together remaining enchilada sauce, fat-free half-and-half, and remaining marinade. Pour sauce over enchiladas and sprinkle top with 1 cup of shredded Monterey Jack cheese.
Bake in preheated oven until the cheese has melted and the top is brown, about 30 minutes.