This more an update than a "reply" to my own post.
I have a P. Cohen arriving in Sydney on Nov 23 1911. The list [part of a crew and passenger list] implies, but does not say, that all those on the list boarded in London [and not en route]. This person is a good candidate for "my" Philip.
However, a search on findmypast for a P. Cohen (or ANY Cohen, for that matter) leaving on the Otranto for Australia in 1911 yielded no one.
One possibility is that the index is incomplete. However, the only way to check this is to find the relevant departure of the Otranto and look page by page through the passenger list.
There are NO other P. Cohens, male or female, in the shipping departure lists on line for any ship that fit the bill as "my" one. All depart either too early to have fathered Jessie's second child or significantly long after Jessie.
In summary, the Otranto person is very likely him, but I would very much like to establish him leaving Britain as well as arriving in Sydney.
-G
