Won't spoil anything, but I think the Jesuit really makes the book. He's often merely a vehicle for the author to show us some neat history and facts, but as a character he's a perfect POV to wrap the story around.

He approaches situations with the logic his Church education instilled in him. He gets some things wrong, but he doesn't conclude anything that an educated man couldn't have figured out 676 years ago, nothing "unnaturally" smart, just smart. The other village priest is more what people imagine how Christians of the time acted and believed.