Heat the oven to 375°F/190°C and cut the cream cheese into small pieces on the counter. The pieces should soften while the remaining ingredients are prepared.
Cut the bacon into thin strips and cook it in a large skillet over medium-high heat. Continue until the bacon is deeply browned and crisp around the edges.
Stir together the garlic powder, onion powder, dried dillweed, Beau Monde Seasoning, and black pepper. The seasoning should look evenly blended before it goes on the chicken.
Trim away any unwanted chicken fat and coat both sides of the breasts with about half of the seasoning mixture. Leave the remaining seasoning for the creamy topping.
Transfer the crisp bacon to paper towels and reserve 2 tablespoons bacon grease in the skillet. Discard the remaining grease and wipe away excess bacon bits if the pan looks crowded with crumbs.
Warm the reserved bacon grease over medium-high heat and sear the chicken breasts for 2-3 minutes per side. The surfaces should brown quickly while the centers remain undercooked.
Move the chicken to a cutting board and slice each breast into 4 or 5 lengthwise strips. Uniform strips create more surface area for the cheese mixture and cook more evenly.
Coat a 9" x 13" casserole dish with non-stick spray and arrange the chicken strips across the dish. Stagger the strips so most of the dish is covered in a single layer.
Place the softened cream cheese in a bowl and microwave it for 20 seconds. It should become very soft and easy to stir without becoming hot.
Finely crumble half of the cooked bacon. Reserve the remaining bacon for a crisp finish after baking.
Mix the softened cream cheese with the crumbled bacon, sour cream, mayo, sharp cheddar cheese, 1/2 cup of the Monterey Jack cheese, and the remaining seasoning mixture. The mixture should be thick, creamy, and spreadable with no large cream cheese pieces.
Spread the cheese mixture over the chicken strips in the casserole dish. Cover the chicken as evenly as possible so the strips stay moist during baking.
Scatter the remaining 1/2 cup Monterey Jack cheese over the top. The cheese should form an even layer that can brown at the edges.
Bake for 20-25 minutes. The topping should bubble around the edges and begin to turn lightly golden.
Thinly slice the green onions while the casserole bakes. Keep the slices ready for a fresh finish just before serving.
Check the thickest chicken strip with a food thermometer before removing the dish from the oven. The chicken should be fully cooked through, with no raw-looking center.
Top the hot casserole with the sliced green onions and reserved crisp bacon. The bacon should stay crunchy against the creamy cheese layer.
Serve the casserole hot. The sauce will be bubbling and cohesive rather than oily when it is ready.