Preheat the oven to 425 degrees F. Remove the stems from 24 large cremini mushrooms.
Wipe the caps clean with a damp paper towel, then toss with 2 tablespoons olive oil and season with salt. Arrange on a baking sheet.
Finely crush 20 butter crackers (such as Ritz); mix with 2 tablespoons melted butter. Melt 2 more tablespoons butter in a skillet over medium heat. Add 1/2 cup each finely chopped celery and red bell pepper; cook until softened, 5 minutes. Add 1 chopped garlic clove; cook 1 minute. Combine 4 ounces cream cheese and 2 tablespoons mayonnaise in a large bowl; add 1/2 cup chopped scallions, 1/4 cup each grated parmesan, cracker crumbs and chopped parsley, the zest and juice of 1 lemon, the celery mixture and 8 ounces lump crabmeat. Divide among the mushroom caps and sprinkle with the remaining cracker crumbs.
Bake 12 to 15 minutes, then broil until golden. Let cool 5 minutes, then remove from the baking sheet.