In a large mixing bowl, combine the softened cream cheese, sour cream, and cottage cheese, stirring until smooth and well blended. Add the cream of chicken soup and mix thoroughly until no lumps remain. Stir in the garlic powder and onion powder, distributing the spices evenly throughout the mixture. This creates a rich, creamy foundation that will coat all the other components.

Add the cooked shredded chicken and cooked rice to the creamy mixture from Step 1, folding gently until everything is evenly combined and coated with the sauce. I like to use a rubber spatula and fold from the bottom up rather than stirring aggressively, which helps keep the rice grains intact and prevents the chicken from breaking apart further.

Preheat your oven to 350°F and lightly grease a 9x13 inch baking dish. While the oven heats, crush the Ritz crackers into coarse pieces (leaving some texture—don't pulverize them into fine crumbs) and toss with the melted and slightly cooled butter until evenly coated. I find that letting the butter cool slightly prevents it from making the crackers soggy before baking.

Spread the combined chicken and rice mixture from Step 2 evenly into the prepared baking dish. Top with the buttered cracker mixture from Step 3, distributing it in an even layer across the surface. Bake uncovered at 350°F for 30 to 40 minutes, until the top is golden brown and the edges are bubbling slightly. The casserole is done when it's heated through and the crackers have turned a deep golden color.