Marinade will work. The flavors given you all will be great with the game hen. Myself, I prefer a brine, which takes much longer, but will flavor the meat all the way through.
My favorite game hens are covered with bacon, stuffed with a rice stuffing (see recipe below), and baked for 12 ninutes a pound at 450'f, or cooked on the covered Webber Kettle, for 12 minutes per pound.
Rice stuffing:
1 stalk celery, sliced
1 small onion, diced
1/2 cup each, cooked wild rice, cooked brown rice (cooked in chicken broth)
6 oz. sauteed mushrooms
1/4 tsp. thyme
1/2 tsp. coarse grind black pepper
1/8 tsp. turmeric
Stuff it into the bird cavity and cook for 15 mintues per pound. Test both the stuffing and the meat with an instant read thermometer. Pull the bird from the heat when the thickets white meat reads 165' F. If you need to, nuke the stuffing in a microwave safe casserole dish.
Seeeeeya; Chief Longwind of the North