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Not sure if you're looking for any other information at this point, but yes, this is a Betts crest. I have an original hand colored, finished version that was given to my grandfather back in the 1950s I believe.  I also have a signet ring with the same image and motto Malo Mori Quam Foedari.  I believe there is a large version of this image or carving in possession of the owners of Wortham Manor, the Betts Homestead in Suffolk (near Diss).  A cousin of mine visited in the 1980s and helped to fund the restoration of the piece that was hanging above the fireplace in that house.  The ownership has changed since then, so I don't know what happened to it.  The Betts family in America did not actually descend directly from the Betts of Wortham, but many of the early 20th century genealogies made that assumption which is why that image is associated with Thomas Betts and his descendants.

Suzanne Betts