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I am no art historian, but the "style" that you are talking about was not limited to gun engraving. Audubon's prints are another example. I wonder if some of his prints were used as models by the engravers - they certainly would have seen them.
The Germans managed some rather cartoonish engraving motifs - I wonder if the Basque makers were simply copying a style they picked up from the German guns they were duplicating (like the Merkel OUs).
Respecting Audubon's prints, it needs be remembered that the animals he depicted were posed in contorted positions so as to fit onto the paper. He was limited thusly because he wanted to present everything life-size. Can you imagine the size of the book necessary to present a blue heron life-sized?
And none of them were posed "from life". Maybe "from recently alive", but not from life.
As to the Germans, a good portion of their animal engraving is very well done, but there was a whole industry of carving and engraving in Germany. Then again, there are those cartoon ducks on the floorplates of some Simsons. Shoulda stuck with foliage and arabesques....
