In a medium bowl whisk the marinade ingredients. Remove the blocks of tofu from their containers, leaving the liquid behind. Cut each block lengthwise into four slices, each about 1 inch thick. Arrange the slices in a single layer on a rimmed platter or in a glass baking dish.
Pour the marinade over the tofu slices and brush the marinade on all sides. Cover with plastic wrap and refrigerate for 3 to 4 hours, turning the slices over once or twice.
In a large bowl combine the salad ingredients and mix well. Set aside at room temperature.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Brush the cooking grates clean. Lay a large sheet of aluminum foil, about 12 by 16 inches, directly on the cooking grates. Lift the tofu slices from the platter and arrange them in a single layer on the foil, reserving the marinade for glazing. Grill the tofu over direct high heat, with the lid closed as much as possible, until both sides are nicely caramelized and the slices are warm, 6 to 8 minutes, turning once and brushing occasionally with some of the reserved marinade. Using a spatula, transfer the slices of tofu to serving plates. Stack the salad on top. Serve warm or at room temperature.