I notice that the spur, however, is missing from the Small Key chip. The C on that chip does still look a bit like a horseshoe.

Still far from an attribution, but looking at newspapers.com the "Hollywood Bit and Spur Club" was in LA at that time.

Ad detail from 7/19/1929, Los Angeles Evening Citizen News;

I will dig around a bit more. Maybe they or another Spur Club used that graphic elsewhere.