To make marinade: Place 1½ cups Florida orange juice and rum in saucepot and reduce volume by ⅔. Combine orange reduction, garlic powder, cumin, oregano, lime juice and black pepper.
Skewer turkey onto sugar cane skewers. Pour marinade over and refrigerate for at least 30 minutes or up to 3 hours.
To make Florida Citrus Sweet-and-Sour Sauce: Combine cornstarch with 2 Tbsp Florida orange juice and reserve. Combine remaining Florida orange, grapefruit and tangerine juices with rice wine vinegar and sugar in small saucepot. Bring to boil and whisk in cornstarch mixture. Simmer until thickened and remove from heat. Allow to cool to room temperature and reserve.
Grill turkey sugar cane skewers over medium-high heat until cooked through. Serve with Florida Citrus Sweet-and-Sour Sauce on the side.