In a small saucepan over high heat, combine the water, 1/4 cup of the rice vinegar, sugar and salt. Bring the mixture to a boil. Stir frequently until the sugar dissolves. Pour the hot vinegar mixture over the radishes. Transfer to the refrigerator to chill, 30 minutes. Drain excess liquid.
In a medium bowl, combine the mayonnaise, ginger, the remaining 2 tablespoons of rice vinegar and sugar. Cover, and refrigerate.
Preheat an outdoor grill to high heat.
In a small bowl, whisk together the soy sauce and chili sauce. Set aside.
Season the fillets with salt and pepper, to taste. Coat the grill racks with cooking spray. Grill the fillets 4 minutes, then brush with half the soy mixture.
Flip the fillets, and grill an additional 4 minutes or to desired doneness. Brush with remaining half of the soy mixture.
Spread 2 tablespoons of the mayonnaise mixture on the bottom of each bun half. Top each with a cooked fillet. Divide the radishes evenly among the burgers. Arrange 2 slices of lettuce on top of each fillet.
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