I took a fluorescent light down over my medicine cabinet because I could no longer get a bulb for it. The wiring was loose in the wall and the box is covered with drywall. If I remove the drywall and open the box, take the wires off running out from the bottom, put a plug in the bottom knock out, and then mount the fixture on the box with a bracket if needed, and fix the hole in the wall they put for the wires, so it was centered over the mirror. I pulled the medicine cabinet. This seems like the best way even though my wife said the light would be better centered over the mirror. I was thinking of replacing the cabinet sometime. I would be satisfied with having the right amount of light and a functional bathroom. All the information I have gotten suggests the best way is to mount the light on the an octagon fixture box. This would mean replacing the fixture box which currently is square.

You can get a 4 inch square to 3 inch round mud ring, see photo: