Bring 2 1/2 cups water to a boil in a small saucepan. Reduce heat, and add kumquats; simmer 1 minute or until tender. Drain; let cool. Remove seeds, and cut kumquats into thin slices.
Combine kumquats, lime juice, and ginger, tossing gently to coat. Set aside.
Stir together vinegar, soy sauce, and shallot.
Scrub oyster shells, and open, discarding tops. Arrange shell bottoms (containing oysters) over crushed ice on a serving platter. Serve with kumquat sauce, vinegar sauce, Fresh Tomato Salsa, and lemon wedges.