I think the explanation is that the apparent falling out of C. Puyo and de Pulligny (artistic temperaments) and the collapse of Darlot, lead to a large number of O d'A makers.
Although Turillon and Ligny are the best known (already active in 1906) there were plenty of others, some with names some without names (yours Jim?). Some have the name Puyo or de Pulligny -without any mention of the other. The quality of the brasswork looks just as splendid as the Darlot engraved types
There have been quite a few of these unknown O d'A and Landscape meniscus varieties sold on that site within the last year and I and others have mentioned them the soft lens sales thread. I thought that some of these may be Darlot unsold stock (and not engraved yet) and sold as special offers!
The "2nd quality" lenses from Darlot and Turillon were undoubtedly engraved!
What is the lens diameter of your 560cm O d'A and does it have 2 symmetrical cells?
I have since learned that my "Photo Amateur" is one of the versions that followed the demise of Darlot.
Photo Amateur was a small shop who like to have their engraving on lenses/cameras. An identically engraved, smaller version, went through ebay last year.