Combine first 5 ingredients. Transfer to a 13x9-in. baking dish; top with cheeses., Whisk together remaining ingredients. Pour sauce over layers, pushing down, if necessary, with the back of a spoon to ensure muffins absorb liquid. Refrigerate, covered, 1 hour or overnight., Preheat oven to 350°. Remove strata from refrigerator while oven heats. Bake, uncovered, until strata is golden and bubbly, 30-40 minutes. Let stand 10 minutes before serving.