The thread title is
Walter W Davies. However, the information that Sandra found matches the poster’s details.

Regarding William adding a middle initial, it could possibly be just an initial not a full name (per the findagrave text). I worked with someone who coincidentally had a middle initial of W. He told me that he didn’t have a full middle name - just the initial. He was very blunt and honest; I believe he was telling the truth about the lack of a name.
The following link appears to be about William’s ship:
https://saintsbysea.lib.byu.edu/mii/account/227Note: I’ve never used the website before; I do not know if it is a trusted site.
Looking at the passenger list on Anc*try, shown under Wm’s(?) and Anne’s names is
Eliz. Do (ditto), age 23, Spinster
Coincidence that she was a Davies, or possibly related to Wm?
The ship arrived in Philadelphia 22 May 1855