Make the dressing: In a bowl, whisk the mayonnaise with the ketchup, relish, lemon juice, garlic, Tabasco, Worcestershire sauce, paprika, and chili powder; season with salt and pepper. Let the dressing stand at room temperature for 15 minutes.
Make the salad: In a medium saucepan of boiling salted water, cook the asparagus until just tender, about 3 minutes. Drain and cool.
Arrange the romaine, cucumber, radishes, tomatoes (if using), eggs, and asparagus on a platter. Top with large chunks of the crabmeat and serve, passing the dressing at the table.
