I'm not aware of a flange to cover it other than the matching one from the mfr. Contact the mfr for an oversized one. Sounds like you got the swivel adapter figured out.
If the electrical box is too deep and sticking out, then get a pancake box which are about half as deep and made for those shallow applications. Try an electrical supplier. Make sure the box is screwed/bolted from two sides or the top so it will support the weight of the fan.
As an aside, make sure any leftover screws aren't the ones the screw the fan blades on. LOL