Make the meatloaf: Mix ground beef, cayenne pepper, black pepper, onion powder, garlic powder, salt, paprika, and oregano together in a large bowl until combined. Shape mixture into a loaf and place on a baking tray; cover with plastic wrap and let rest in the refrigerator overnight.
Preheat the oven to 350 degrees F (175 degrees C).
Bake meatloaf in the preheated oven until no longer pink in the center, about 30 minutes, turning the loaf over halfway through cooking. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C). Allow the meatloaf to cool so it holds together for slicing.
Meanwhile, make the sauce: Stir evaporated milk and sugar together in a bowl until sugar is dissolved; add vinegar, 1 teaspoon at a time, to taste. Refrigerate sauce until ready to serve.
Slice meatloaf into 1/4-inch thick slices; brown each slice in a skillet over medium heat until browned and crisp, about 5 minutes per side.
Sprinkle pita bread rounds with a little water; warm briefly in a dry skillet over medium heat.
To serve: Place several slices of meatloaf into each warmed pita bread; spoon about 2 tablespoons of sauce on top and roll into a cone shape. Wrap each donair in aluminum foil to keep the sauce from dripping out; serve.