Maybe the crew was researching the historic development of anchors rather than the history of exploration of that coast.
I’m thinking it came from an Alaska Packers ship. A hundred years ago the Alaska Packers Association operated some of the last working square-rigged ships in the USA. They sent them north from Alameda in the summer with fisherman and supplies to the the big Bristol Bay salmon rivers, where the ships would anchor out until the catch was over. Then they would load the canned salmon aboard the ships and sail back to California.
So, 1890-1930, not 1600 (guess). The archaic patter of the anchor would match these ships well. The striated pattern of rust on the anchors links shows they are made of iron, rather than steel. Meaning they were holdovers from the 19th-century, as were the ships. One of the Alaska Packer ships remains: Balclutha in San Francisco.
I think the Star of India, currently in San Diego was an Alaska Packer shop as well - she’s iron instead of wood, but still actively sailing.