Preheat the oven to 400°F.
Lightly butter a baking dish or individual casserole dishes.
Place 3 tablespoons butter in a skillet. Place over medium heat.
When butter has melted and is hot (do not burn), sauté celery, onion, and bell pepper for 2 minutes, just until softened. Transfer to a plate. Place in the refrigerator to chill briefly.
Finely chop half of the mushroom stems. Discard the rest or save for another use.
In a mixing bowl, combine chilled sautéed vegetables, chopped mushroom stems, crab meat, crushed oyster crackers, both cheeses, garlic powder, Old Bay seasoning, black pepper, salt, Worcestershire sauce, egg, heavy cream or water and lemon juice. Mix well until the filling is moist but holds together.
Arrange mushroom caps in the prepared baking dish(es), cavity side up.
Spoon about 1 teaspoon of filling into each mushroom, gently pressing to shape.
Tear or cut the white cheddar slices and drape over the stuffed mushrooms.
Place in preheated oven and bake for 12 to 15 minutes, or until the cheese is melted and lightly golden.
Turn oven to broil and, watching closely, broil for 1 to 2 minutes to give the cheese a bubbly, golden crust.
Serve warm with a squeeze of lemon or a drizzle of melted garlic butter.