One possible line of inquiry would be to focus on the operators of _SS Kaiser Wilhelm II_ , the **Norddeutscher Lloyd** line (NDL).
My working assumption would be that in the early 1900s, people able to make regular trans-atlantic voyages had a favourite line (or even a favourite ship) which they used repeatedly.
It is possible that the Fosters et al made the easterly crossing on an NDL ship as well. So by finding when the _Kaiser Wilhelm_ (or the _SS Kronprinz Wilhelm_ , or the _SS Kronprinzessin Cecilie_ ) made runs from Hoboken to Bremerhaven in 1911, you will have identified a subset of records to search for.