I've found the last missing date for the voyages of the "Julia Ann". On her third return voyage from Sydney to San Francisco, she arrived in San Francisco on April 12, 1855. Her voyage took 78 days. Here is the shipping notice:

http://cdnc.ucr.edu/newsucr/cgi-bin/newsucr?a=d&cl=search&d=DAC18550413.2.22&srpos=191&e=-------en-logical-20--181-byDA---Barque

And here is an advertisement for her first voyage in April of 1853:

http://cdnc.ucr.edu/newsucr/cgi-bin/newsucr?a=d&cl=search&d=SDU18530314.2.2.2&srpos=167&e=-------en-logical-20--161-byDA---JULIA

And here is the complete schedule of her voyages:

Voyage #1   
        Departed San Francisco April 12, 1853.
        Arrived in SydneyJune 22, 1853.
        Departed Sydney on or about August 25, 1853.
        Arrived in San Francisco on October 12, 1853.

Voyage #2
        Departed San Francisco on December 2, 1853.
        Arrived in Sydney on January 24, 1854.
        Departed Sydney on March 22, 1854.
        Arrived in San Pedro CA on June 13, 1854. (83 days)
       Arrived in San Francisco shortly thereafter.

Voyage #3
        Departed San Francisco July 26, 1854 for Puget Sound
       Departed Puget Sound October 8, 1854.
        Arrived in Sydney on December 5 1854.
        Cleared for San Francisco, via Newcastle on December 21, 1854
        Departed Newcastle for San Francisco on January 17, 1855
        Arrived in San Francisco on April 12, 1855 (78 days from         Sydney)

Final Voyage #4
        Departed San Francisco May 19th, 1855.
        Arrived in Sydney on July 24, 1855.
        Departed from Sydney on Friday, September 7th, 1855.
        Ran aground and sank off the Scilly Islands on October 3-4, 1855.  

I've just found this site for searching California newspapers. I've spent most of the day trying to find something on "chanties", "sea songs", "work songs", "sailor songs". But so far I have not turned up a thing! It is a bit frustrating because I haven't exactly figured out the best way to phrase my searches.