Stir together brown sugar and next 4 ingredients in a small saucepan over medium heat, stirring constantly, until blended. Cook over low heat, without stirring, 10 minutes or until sauce begins to thicken. Remove from heat; keep warm.
Cut pineapples lengthwise into fourths, leaving crown ends on. Remove hard core from each quarter; cut pineapple pulp away from shell in one wedge-shaped piece, keeping the crown and shell intact. Set pineapple shell aside. Cut pineapple wedge into 8 equal crosswise slices, and thread onto wooden skewers. Repeat procedure with remaining wedges.
Spray food grate with cooking spray, and place on grill. Place pineapple on grate. Grill, covered with grill lid, over medium-high heat (350° to 400°) 4 minutes on each side or until thoroughly heated.
Arrange skewers in reserved pineapple shells, and drizzle with warm rum mixture.