Prepare rice according to package directions, set aside.
Combine cornstarch and water, stirring well, set aside.
Melt butter over medium heat in a heavy saucepan; stir in teriyaki sauce, lemon juice, sugar, 1/4 teaspoon pepper, and ginger.
Gradually stir in cornstarch mixture.
Cook, stirring constantly, 1 minute or until smooth and bubbly, set aside.
Remove giblets from hens, reserve for another use.
Rinse hens with cold water, and pat dry; sprinkle with 1/2 teaspoon pepper.
Stuff hens with rice, and close cavities.
Secure with wooden picks, truss.
Place hens, breast side up, in a shallow baking pan.
Bake at 375° for 30 minutes.
Baste with teriyaki sauce mixture, and bake an additional 40 minutes, basting every 15 minutes.