Flip that box around so it faces inside the closet, use it as a junction box, cover it with a blank plate,and run flexible cable to a new box in the location you want.

Drill a small hole ⅛ inch or smaller (just big enough to slide a single thin wire) in the hardwood right up against the base board. Measure about 2-2½ inches towards the wall you're trying to get into. After your done fill the small hole in the hardwoods with putty.