A good hvac man can fix that in a few hours.You just cut out 18" of base out and cut in a 2 1/4 x 12 0r 14" opening flush with the sheetrock use a 2 1/4"x 12 or 14" x 6" 90 degree boot and tie it into the existing feeder that is feeding the floor register ( most likely a 6" round ).hole in the floor.Then patch the floor register hole.Well maybe you had just better call the HVAC guy.LOL
Good luck. By the way Hart & Cooley makes those baseboard registers Called B-18