This is a small project, so it is easy to clean up. I decided to go back to steel wool to rough up the first coat of urethane. I like the steel wool better than the scotch-brite pads, but it leaves a lot of broken pieces of wool behind. After everything had been sanded, I cleaned it off with some compressed air and I checked to make sure no bits of steel wool were stuck in the corners.
I applied the second coat of poly and let it sit over night to cure.
When everything was dry, I attached the hanger wire and it was finished.
There is a bit of tension on the hinge, but if the new owner has a problem with the door coming open, I will epoxy a small magnet on the right side of the box and match it to a screw on the back side of the frame.