The patchbox fit is the elephant in the room. The bottom finial appears to fit the BP well. The door seems to be one of those that cuts the BP, fair enough, but seems too long, and the top finial seems to be a terrible fit. But it also seems that the door and upper finial are slightly bent - which could explain their appearance, given the angle of the photo.
A photo from a different angle would tell SO much. Easy thing to remove the BP and box and see what's going on there.
The eagle engraving and box engraving seem to be similar in level of skill, but impossible to tell from the photos if they're the same hand, but somehow I doubt it. The small shield is very naiively done, and it makes me wonder how many pairs of hands have been monkeying with this gun.
Once again, mediocre photos start more wars than Helen of Troy.