As I go through this somewhat strange exercise of testing the
Double Wedding Band model with a look at
potential connections of the seven Harry Potter books with the last seven Strike books. one thing that is becoming clear to me is that some of the clearest thematic connections turn up in the openings of the books. See
here,
here and
here for examples. In a way, this makes sense, given that some of the most obvious examples of chiastic structure in the Harry Potter series show up in the opening Dursley segments. See the illustration from my chapter on humor in Harry Potter from
Harry Potter, the Ivory Tower and Beyond for examples.
Happily, as I started my look at The Goblet of Fire and The Running Grave, I saw that this pairing is no exception. The most notable similarity is that both books start with a somewhat unusual point of view, one of someone other than the protagonists. Goblet of Fire sets up the main storyline by providing first a newsreel-like history of the Riddle family murder in Little Hangleton, followed by the suspicion cast on Frank Bryce and his subsequent discovery of Wormtail and Voldemort hiding out in the old Riddle house. Interestingly, though the end of the scene cuts into Harry Potter's scar-tingling nightmare that he presumably sees through the mental link with the Dark Lord, the narrative presented to the readers is from the perspective of Frank Bryce, including events and thoughts of which Voldemort was unaware. Chapters from the perspective of someone other than Harry are very rare in the Potter series, occurring only in the first chapters of books 1, 4 and 7 and in the first two chapters of book 6.

The Strike series is also usually from the perspective of one of the lead detectives, although other perspectives are more common than in Harry Potter. For example, Book 3 has multiple chapters from the killer's perspective, while Book 6 shows many online chats among the moderators of Drek's Game.
The Running Grave opens with a Prologue setting up the detectives' major case, delivered through a series of letters between Colin and Sally Edensor, their son Will, eventual murder victim Kevin Pirbright and Edensor's lawyer, along with some interview excerpts with church principals Noli Seymour and Giles Harmon.
Both of these opening, alternate-perspective segments end with a relatively abrupt death. Frank Bryce, like the Riddles of fifty years prior, is Avada Kedavra'ed by Voldemort, and therefore "is dead before he reached the floor." Sally Edensor succumbs fairly quickly to her brain tumor, even though "the doctors thought she had longer." Although neither of these deaths is the major murder our heroes will eventually solve in these books, the story of both deaths is used to set up the major storyline.