Does the old work box really stick out that far? Doesn't seem like the tabs that hold it against the drywall would cause that huge a gap. Tightened down well it should be nearly flush.

Try bending the sides of the mounting plate the lamp screws into back so when you attach it to the box they sit closer to the wall.

Is there a window you could pass it through? You can cut a pool noodle or piece of pipe insulation to width stick that in there and shut the window on it to seal the gap around the cord.