Tom, I have looked into my NYC Passenger Equipment Diagrams (original edition 12/1/1939, plus various subsequent revisions) in an attempt to answer your question. I recall having seen at least one of these cars on an occasion in the late 1950s at GCT; these cars were NYC #97, 98, and 99. They were modified from the arch-roof cars built by Osgood Bradley in 1927 for use on the B&A. The diagram page shows an undated pencil entry as "steel, club" appearing on a revision page dated 12/31/42.
These cars replaced three other cars (71, 73, and 76 that were stricken - also in pencil). Those three cars are indicated as having been built by AC&F in 1912, each with a conventional clerestory.
The reference diagram is for the B&A coach (no toilet); unfortunately I have no floor plan.