You might start by visiting the website of the Maratime Museum in Kingston, NY...While there archives are mostly on the Hudson River Steamers, they do have other info at times..
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Sounds like some pretty neat research you're doing. I wasn't able to find anything in the National Archives catalog related to the H. J. Corcoran, the California Navigation & Improvement Company, or safes that were used during that time. Mine was a cursory search though.
I did find the following records for the Steamboat Inspection Service: https://catalog.archives.gov/search?q=steamboat%20inspection%20service
I would recommend starting in Record Group 41 and the Records of Vessel Inspections and Certificates Issued, 10/25/1882 - 7/20/1933. They are held in the National Archives at Riverside get in touch with them and see if they can provide some assistance.
National Archives at Riverside (RW-RS)
23123 Cajalco Rd
Perris, CA 92570