To prepare marinade, combine first 5 ingredients in a large zip-top plastic bag. Trim fat from steak, and add steak to bag. Seal and marinate in refrigerator at least 2 hours, turning bag occasionally. Remove the steak from bag, reserving marinade. Pour the marinade into a microwave-safe dish. Microwave marinade at HIGH 1 minute or until mixture boils.
To prepare flavored mayonnaise, combine mayonnaise and horseradish, and set aside.
Place steak and red onion slices on a grill rack, and grill onions 4 minutes on each side, basting with the reserved marinade. Remove onions from grill. Turn the steak, and grill an additional 8 minutes or until steak is desired degree of doneness. Remove steak from grill. Place bread slices on grill rack, and grill 2 minutes on each side or until toasted.
Cut steak diagonally across grain into thin slices. Spread 1 tablespoon flavored mayonnaise on one side of each of 8 toasted bread slices. Divide steak, onion slices, lettuce, and tomato slices evenly among 8 bread slices. Top with remaining bread slices.
Note: Substitute pineapple juice for rum, if desired.