Pat the chicken breasts completely dry and season all over with the salt, black pepper, garlic powder, onion powder, smoked paprika, cumin, chili powder, cayenne, and the full 1 oz packet of taco seasoning.
Heat the olive oil with 2 tbsp of the butter in a pan over medium-high and sear the chicken 3 minutes per side until the crust darkens. It will not be cooked through yet, but the sear is what gives the finished dish depth instead of a flat boiled taste.
Move the chicken to the crockpot. Add the remaining 2 tbsp butter to the pan over medium and cook the onion and both bell peppers 5 minutes until softened, scraping the bottom clean as it loosens.
Add the minced garlic and cook 45 seconds until fragrant, then pour in the chicken broth and scrape every browned bit off the pan.
Pour the mixture over the chicken and add the salsa, the diced tomatoes with green chilies and all their liquid, and the bouillon powder. Do not add the beans or corn yet, they will break down over a long cook.
Cover and cook on low 5 to 6 hours or high 3 hours, until the chicken pulls apart with no resistance.
About 30 minutes before serving, rinse the rice until the water runs clear, then combine with 3 1/2 cups water, 1 tsp salt, and 2 tbsp butter. Bring to a boil, cover, drop to the lowest heat, and cook 16 minutes.
Pull the rice off the heat and leave it covered and untouched 10 minutes, then fluff with a fork so the grains stay separate and loose.
Lift the chicken out of the crockpot and pull it into thick tender strands with two forks, leaving them chunky rather than fine.
Add the cream cheese cubes to the hot liquid and stir every couple of minutes for about 8 minutes until fully melted and completely smooth, then stir in the heavy cream.
Add the black beans and corn, cover, and cook 15 minutes more until heated through.
Switch the crockpot to warm and stir in 1 cup of the Monterey Jack, 1 cup of the cheddar, and 1/2 cup of the Parmesan in handfuls, letting each melt before the next goes in. Cheese added on high heat turns the sauce grainy.
Stir in the sour cream and lime juice off the boil, then return the pulled chicken and all its juices and fold everything through.
Scatter the remaining Monterey Jack and cheddar over the top, cover, and leave on warm 8 minutes until it melts into gooey stretchy patches sitting visibly on the surface.
Spoon the rice into white bowls, pile the fiesta chicken over the top and mix some through so the sauce runs down between the grains, and finish with the remaining Parmesan, cilantro, and green onions.