The kind folks at JA Henckels in Germany came back with a quick reply. Here's what they said:
Thank you very much for your mail to my colleagues in the US.
In an old catalogue from the year 1922 we found a razor set similar to yours (see enclosed copy).
This item was a special edition for our subsidiary in the US, TWIN WORKS, located in New York.
Mit freundlichen Gruessen / Kind regards
ZWILLING J.A. Henckels AG
i.A. Bettina Thomas
Archiv / Archive
The file they sent doesn't have the exact set I have, but it's close.