So far, I have found only a few bits of information on Captain Millett. He was "of Cutty Sark fame and a member of the Port of London Authority," wrote something in 1927, and had a theory about the disappearance of the ship "Celeste", with the suggestion "that the Celeste had been boarded by pirates of the Rif (the coastal region of Morocco..." He died at Penzance. (From snippets on Google Book Search). He wrote a book entitled YARNS OF AN OLD SHELLBACK published in 1925. I don't have access to that book.

In her book, A BOOK OF FAMOUS SHIPS, C.F. Smith has a chapter on the "Cutty Sark", but does not mention Captain Willett. She does talk about a Captain Willis, but I don't think that they are the same person. In a very quick scan, I was not able to find any other references in this book to Captain Willett, but I may have missed them. Here is the link:

http://books.google.com/books?id=gYadeUzJnh8C&pg=PP1&dq=A+Book+of+Famous+Ships&lr=&cd=1#v=onepage&q&f=false

So, I haven't come up with any more on either Captain Willett or his song "Bound to California".