Scrub clam shells and mussels well with a brush; remove beards from mussels. Discard opened or cracked clams and mussels. Peel shrimp, leaving tails intact, and devein. Drain crabmeat, and remove any bits of shell. Set aside.
Melt butter in a Dutch oven over medium-high heat. Add garlic and next 7 ingredients; sauté 4 to 5 minutes or just until tender. Add rice and tomato; stir well. Add chicken and fish broths; bring to a boil. Cover, reduce heat, and simmer 12 minutes.
Add clams, and cook 5 minutes. Add mussels and shrimp; cook 5 minutes. Stir in crawfish; cook 5 to 7 more minutes or until clams and mussels have opened. Discard any unopened shells. Stir in crabmeat and parsley. Remove from heat, and let stand 2 minutes. Discard bay leaf. Serve immediately.