Bring wine, chicken broth, beef broth, thyme sprigs, and bay leaf to boil in heavy large saucepan. Boil until reduced to 1 cup, about 35 minutes. Mix butter and flour in small bowl to blend. Whisk butter-flour mixture into broth. Simmer until slightly thickened, about 2 minutes. Stir in lingonberry preserves; simmer 1 minute. Remove thyme sprigs and bay leaf. (Sauce can be made 1 day ahead. Cover and refrigerate. Rewarm before serving.).
Spray 8x8x2-inch baking dish with nonstick spray. Heat 2 tablespoons olive oil in heavy large skillet over medium-high heat. Add garlic; stir until beginning to brown, about 30 seconds. Add all mushrooms; sauté until soft, about 5 minutes. Add chicken broth; bring to boil. Gradually whisk in polenta. Reduce heat to medium and cook until polenta is tender and mixture is very thick, stirring frequently, about 10 minutes. Stir in truffle oil. Season to taste with salt and pepper. Transfer to prepared pan, spreading evenly. Press plastic wrap onto surface of polenta. Refrigerate until cold, at least 2 hours. (Can be made 1 day ahead. Keep refrigerated.).
Prepare barbecue (medium-high heat). Preheat oven to 450°F Score skin of duck breasts in crisscross pattern (do not cut through to meat). Sprinkle duck with salt and pepper. Heat heavy large ovenproof skillet over high heat. Add duck breasts, skin side down, to dry skillet. Reduce heat to medium and cook until skin is golden brown, about 7 minutes. Turn duck over and transfer skillet to oven; roast to desired doneness, about 5 minutes for medium-rare. Using tongs, transfer duck to cutting board; tent with foil. Let stand while grilling polenta.
Cut polenta into 6 rectangles; brush both sides with additional olive oil. Grill until warm and slightly charred, about 3 minutes per side. Place 1 polenta rectangle on each of 6 plates. Cut duck breasts crosswise into 1/2-inch-thick slices; fan 1 duck breast over polenta on each plate. Drizzle with sauce and serve.
*Sold at Italian markets, natural foods stores, and some supermarkets. If unavailable, substitute regular yellow cornmeal and cook for about half the time.