@Ian Simpson I think you are almost there. The only thing that stands out is the transition of the armrests to the front lip of the chair. The transition is rounder than what you have. Look at the closest Burke 116 in this screenshot:
http://tos.trekcore.com/hd/albums/1x13hd/theconscienceofthekinghd277.jpg
http://tos.trekcore.com/hd/albums/1x13hd/theconscienceofthekinghd277.jpg