Preheat the oven to 350°F. In a mixing bowl, combine the breadcrumbs, Pecorino-Romano, lemon juice, olive oil, melted butter, chopped parsley, salt, pepper, oregano, garlic powder and smoked paprika. Mix well. Evenly divide the breadcrumb mixture into three bowls. Leave one bowl as is. Add the crabmeat to one of the bowls and toss to combine. Add the salmon to the last bowl and toss to combine. Split up the mushrooms and fill each one with the different stuffing mixtures. Melt the butter and spoon over the mushrooms. Bake for about 15-20 minutes until golden.
In a small saucepan, heat the oil over medium heat. Add the shallots and sauté until soft. Deglaze the pan with the champagne. Bring the liquid to a boil and then reduce to a simmer. Let simmer for about 30 minutes. Let the champagne mixture cool slightly and transfer it to a mixing bowl. Whisk in the Dijon mustard and then slowly drizzle in the oil, whisking continuously until incorporated. Stir in the tarragon, salt and pepper.
Combine the mayonnaise, lemon juice, lemon zest, fresh dill, salt and pepper in a mixing bowl. Whisk until incorporated.
In a small saucepan, add the butter and garlic. Melt the butter over medium-low heat while the garlic infuses.
Serve the mushrooms on a large platter with the champagne vinaigrette, dill mayo, and garlic butter alongside.