This was clearly a case for a third-person omniscient narrator.
The book uses a third-person narrator who is nevertheless close with the characters' emotions.
On other occasions we detect language which can only be that of James, the third-person narrator.
The rest of the book is Billy Pilgrim's story told by a third-person narrator.
The limited third-person narrator, on the other hand, doesn't fly freely over the landscape.
The limited third-person narrator can never change viewpoints in mid-scene.
A limited third-person narrator would also be forced to show us the scene from only one character's point of view at a time.
For stories in which the context and the views of many characters are important, a third-person narrator is a better choice.
A third-person narrator works wells for stories in which the viewpoints of many characters is important.
The majority of the novel is told through a third-person omniscient narrator.