Nick: In the light of the EFDSS declaration how do they get the right to charge anybody for the photos?

I read the declaration, differently...apparently. It's mostly disclaimer. Perhaps lost in translation but, exactly wherein is the EFDSS first party claim of copyright? Have either Getty or Heritage made any copyright claims against publishers?

If the rights are still with the Sharp family, how did your second party application address that first line:
I acknowledge that it is my responsibility to obtain any necessary third party consent to reproduce the items supplied by the Library from the owner of any such copyright in the materials, and I enclose a copy of such consent.

I think we're conflating/confusing physical property, access and copyrights old & new.

One may reproduce old photographs but not new reproducitons of same. The actual thing used in the new production stream must also be out of copyright. ie: Clipping a 1920 image from a book published in 2020 can get one it hot water (if found out.)