Begin by making the pizza dough: Add all the ingredients to your bread machine, in the order suggested by the manufacturer. Select the dough cycle and press start.
While the dough is being made in the bread machine, make the Alfredo sauce: In a large skillet, melt the butter. Add the onion and garlic and cook about ten minutes or until the onion is soft. Add the cream and milk and cook on medium heat until the mixture thickens, about ten minutes. Stir in the Parmesan cheese and cream cheese.
As the Alfredo cooks, bake the chicken, mushrooms, and bacon: Preheat the oven to 400 degrees. In a bowl, toss together the chicken, mushrooms, oil, lemon juice, oregano, garlic powder, kosher salt, and pepper. Place it all on a rimmed baking sheet along with the bacon. Bake for 15 minutes. When it's done, chop the chicken and bacon into half or quarter inch pieces.
When the dough cycle is done, dump the dough on a floured board, and cut it in half. Roll each half into two 12 inch circles, on parchment covered baking peels. Brush the doughs with olive oil, and cover them with plastic wrap. Let them rise for 30 minutes. Preheat the oven to 425 degrees.
Top the dough with first the Alfredo sauce, and then sprinkle on the tomato, chicken, mushrooms, and bacon.
Using the pizza peels, slide the parchment and dough onto the pizza stones. Bake for 15 minutes. Then, add the cheese and bake for five more minutes.