I'm intrigued. Why is this a case of 'double possessives' as opposed to a punctuation issue?
As I understand double possessives:
Do we say "a friend of my uncle" or "a friend of my uncle's"? We distinguishing between "a picture of my father" (in which we see the father painted in all his glory) and "a picture of my father's" (a picture that the father owns).
I can't see how a construction such as "St. Paul's Cathedral's vergers" (whether a construction approved of or not) compares to your example. And similarly, 'friends of my sister' or 'my sister’s friends'
Where are we miles apart on this?