Preheat your oven to 400°F (200°C) and lightly grease a 9 by 13 inch baking dish.
In a large bowl, stir together the 2 cups shredded chicken, 1 cup corn, 4 ounces cream cheese, 5 tablespoons sour cream, ½ cup Mexican cheese, ½ cup mozzarella, 1½ tablespoons taco seasoning, ½ teaspoon garlic powder, 1 teaspoon chili powder, the juice of 1 lime, and the 4 ounces green chiles until creamy and well combined.
Brush one side of each tortilla with a little of the 2 tablespoons oil. Flip them oiled side down, spoon about 3 tablespoons of filling onto each, add a pinch from the ½ cup shredded cheese, and fold into a half moon.
Pack the folded tacos snugly upright in the dish so they hold their shape. Bake for 10 to 12 minutes, until golden and crisp and the cheese pulls when you tear one open.
While they bake, stir together the ¼ cup sour cream, 1 tablespoon lime juice, ½ teaspoon taco seasoning, and a few dashes of hot sauce for the dip.
Finish the tacos with a sprinkle of the chili powder and lime mix, a scatter of crumbled feta, and chopped cilantro. Serve hot with the dip alongside.