1. Combine first 6 ingredients in a large zip-top plastic freezer bag; add turkey. Seal and chill 4 hours, turning occasionally.
2. Preheat grill to 350° to 400° (medium-high) heat. Coat cooking grate with cooking spray, and place on grill. Remove turkey from marinade, discarding marinade.
3. Grill turkey, covered with grill lid, 20 to 25 minutes or until a meat thermometer inserted into thickest portion registers 170°, turning occasionally. Let stand 15 minutes. Cut turkey diagonally into thin slices, and arrange on a serving platter. Season with salt to taste.