1. Combine the wine, vinegar, oil, tamari or soy sauce, garlic, oregano, basil, and parsley in a zip-close plastic bag; add the mushrooms. Squeeze out the air and seal the bag; turn to coat the mushrooms. Refrigerate, turning the bag occasionally, at least 6 hours or overnight.
2. Spray the grill rack with nonstick spray; prepare the grill for medium-hot fire.
3. Pour the marinade into a small saucepan and boil, stirring constantly, 3 minutes.
4. Grill the mushrooms, stem-side down, 5 inches from heat, turning occasionally, until golden brown on both sides, about 7 minutes. Pour the cooked marinade over the grilled mushrooms and serve.