Preheat the oven to 375°F (190°C). Line a rimmed sheet pan with parchment paper or aluminum foil.
Place the mushroom caps on the baking sheet, evenly spaced, stem-side up. Season with 1/2 teaspoon salt.
In a medium bowl, mix together the crabmeat, cream cheese, 2 tablespoons of the chopped parsley, the green onions, 2 tablespoons of the Parmesan cheese, and the garlic powder and dried herbs. Stir in 1 teaspoon salt and 1/4 teaspoon pepper.
Stuff the mushroom caps with rounded tablespoonfuls of the cheesy crab mixture. Evenly space the stuffed mushrooms on the prepared sheet pan. Brush or drizzle each mushroom with the melted butter. Top the mushrooms with the remaining 2 tablespoons Parmesan cheese, then bake until the filling is hot and melted and golden on top, about 25 minutes.
In a small bowl, toss together the remaining 2 tablespoons chopped parsley and lemon zest. Sprinkle the lemony mixture over the mushrooms and serve.