Combine the first 15 ingredients in a large zip-top heavy-duty plastic bag. Seal the bag, and marinate in the refrigerator 24 hours, turning the bag occasionally.
Remove the venison from the bag, and discard the marinade. Place the venison on a broiler pan coated with cooking spray, and broil 10 minutes on each side or until done.
Cut the venison crosswise into thin slices.