Preheat oven to 400°F. Bring stock to a boil in a Dutch oven over high. Add chicken to stock. Cover; reduce heat to medium. Cook until a thermometer inserted in thickest piece of chicken registers 160°F, about 25 minutes. Remove chicken; let stand until ready to use. (Inner temperature of chicken will rise as it stands.)

Return stock to a boil over high. Add pasta to Dutch oven, and cook until just tender, about 9 minutes. Transfer pasta to a medium bowl (reserving stock). Return stock to a boil over high; boil until liquid is reduced to about 2 1⁄2 cups, about 1 minute. Whisk together evaporated milk and flour in a small bowl. Stir into stock; boil until slightly thickened, 2 minutes. Remove from heat; stir in Worcestershire sauce, hot sauce, and salt. Pour stock mixture over pasta.

Return Dutch oven to medium-high heat. Add butter, onion, and bell pepper. Cook, stirring often, until tender, 5 to 6 minutes. Remove from heat; add pasta mixture back to Dutch oven. Shred chicken, discarding bones. (You should have about 4 1⁄2 cups meat.) Add chicken and tomatoes to Dutch oven; toss to coat. Pour mixture into a 13- x 9-inch baking dish coated with cooking spray. Top with cheese. Lightly coat aluminum foil with cooking spray. Cover with foil; bake until cheese is melted, 25 to 30 minutes.