Combine the Masa Harina with the remaining 1/2 cup stock and mix to blend. Slowly add to the pot, stirring to blend. The mixture will thicken. Cook for 30 minutes, then season again with salt and cayenne. It should be thick enough to coat the back of a spoon.
In a heavy, deep pot or an electric fryer, heat 4 inches of vegetable oil to 360 degrees F. Fry the shoestring potatoes in batches until golden brown, 3 to 4 minutes per batch. Drain on paper towels, then season with salt and cayenne.
Preheat the oven to 400 degrees F.
Cover the bottom of a large, glass rectangular baking pan with the shoestring potatoes.
Combine the Cheddar and jack cheeses. Sprinkle the cheese over the fries.
Bake just until the cheese melts, 3 to 4 minutes. Remove the pan from the oven and spoon the chili over the top of the fries. Garnish with the sour cream and jalapenos. Serve immediately.