Place steak in a large zip-top plastic freezer bag.
Combine 1 cup soy sauce, pineapple juice, and next 4 ingredients, stirring until sugar dissolves; pour over steak. Seal bag, and chill at least 1 hour or up to 8 hours, turning occasionally. Remove steak from marinade, discarding marinade.
Grill steak, covered with grill lid, over medium-high heat (350° to 400°) 5 minutes on each side or to desired degree of doneness. Let stand 10 minutes before slicing; cut steak diagonally across the grain.
Note: For testing purposes only, we used McCormick Caribbean Jerk Seasoning.