Drain tofu, cut into slabs, wrap in plastic and freeze until firm.
Lightly coat baking sheet with sides with nonstick cooking spray. Place tofu slabs on prepared sheet.
In blender, mix marinade ingredients until smooth. Spoon over tofu slabs; turn to coat and marinate 1 hour.
Meanwhile, in small saucepan, mix tomato sauce, onion, brown sugar, parsley, molasses, salt, allspice and cayenne. Bring to a boil, reduce heat to low and simmer, stirring occasionally, 1 hour. Stir in lemon juice and liquid aminos.
Preheat oven to 350°F. Bake tofu 25 minutes per side. Brush barbecue sauce over both sides of baked tofu and bake until hot, 15 to 20 minutes more.