CooleyS, your engraving of the buffalo fits right in with the two original buffalo-engraved Hawken patchboxes I've seen. Both of the originals (and every other animal-engraved Hawken/Campbell patchbox I can think of) has some sort of "background". In the deer patchbox you posted, it would be the plants, ground under the deer, etc--something like that might be what you're thinking.
I'm probably overlooking something somewhere, but the only animal-engraved Hawken patchbox I can recall offhand that has a border engraved on the door is a brass-mounted "squirrel rifle" presumably made for the local trade. It has a couple of deer, with a border (like on the deer patchbox you posted) engraved on the door. It always looked "odd" to me and I wonder if this was why?