This one is really interesting. I wish I had thought about it before some others had gone down their respective paths, because I believe The Conjuring (or an "offshoot" of The Conjuring) is the correct path from what my head is telling me. I know some others have theorized The Conjuring already, so my apologies to those folks if I'm reiterating some of your notes.
* The clue is indeed the Coat of Arms for Francis Patrick Keough
* Francis Patrick Keough was born in Connecticut and was the Bishop of Providence, Rhode Island
* Lorraine Warren was born and died in Connecticut.
* The house that inspired The Conjuring is located in Rhode Island.
** So that's 2 connections to Francis Patrick Keough and The Conjuring
* Now, the fact that the clue itself is a coat of arms for a clergyman points me through The Conjuring and directly to The Nun (remember that Legacy warned us that the clues can lead to an answer that is simply another clue - The Conjuring could be the answer to part of the clue, but not the final answer).
* The Nun follows a Roman Catholic priest and a nun in Romania. Francis Patrick Keough was part of the Roman Catholic Church, so there is a general connection there.
* The Nun also has a very gothic feel to it. Coats of Arms generally have a gothic feel to them as well.
* The saying at the bottom of the Coat of Arms is "Maria Spes Nostra", which translates to "Mary, our hope". One of the more famous prayers in Roman Catholicism is "Hail Mary", which stems from that fact that Roman Catholics believe Jesus to be our savior (or hope). Mary Magdalene was the mother for Jesus in Roman Catholicism, thereby making her our hope and savior by the transitive property. So that's where the "Mary" part of the clue ties into the religious aspect which transcends The Conjuring through to The Nun.
* So, for me, the dual connection of Keough to The Conjuring through similar birth state to Lorraine Warren and the fact that he was the Bishop of a state which housed the inspiration to The Conjuring. Then, the religious aspects come into play to take it from The Conjuring to The Nun. The Nun also performed VERY well at the box office and, coincidentally, there is a sequel in the works right now that is scheduled to release this October.
Now, the fact that The Nun is a Warner Brothers film is an issue that I cannot explain away and makes me think this is off base. However, MAYBE the fact that the sequel is releasing at the end of October, Warner Brothers makes a deal with Universal to allow the property at HHN 30 which, in turn, will RAISE the profile of the release and Warner Brothers pulls in more money from the movie BECAUSE of HHN. That might be more off track, but there are enough connecting factors here for me to take the swing and guess The Nun as the final answer to this clue.