The story seems at first to be very realistic - the narrator refers to himself as a novelist, as if the story is an account of something that happened to the author himself, perhaps recently. It continues completely normally until Duarte's dead daughter is unearthed, not decomposing, after 11 years, and "her body had no weight."
The story is structured within the context of the present, with some summary of past events (e.g. above), some of which the narrator is not present for. I would expect, for this reason, that the film adaptation would be from a third person point of view, likely without narration, less focused on the narrator as the main character. Rather, I expect that it would follow the story as the narrator tells it, but not through the same voice.
I wonder, however, if the filmmaker might have decided to restructure the narrative linearly, so that it begins with Duarte's story straight away, and end up in the cafe. It would not be a necessary choice, but a possible one. Or perhaps it could start in the cafe, have Duarte open the box with his pristine daughter inside, and then go back in flashback to explain why.
To expand the narrative, I would guess that the film would go more into depth with the story of the wife and the daughter dying, and then take it from there. Of course, this is not necessary either - it could easily be filmed with the same level of detail as in the story, perhaps a few shots summarizing the past, before Duarte is in Rome with the girl's body.
The Pope's hiccuping problem is quite funny.
The juxtaposition of a magical, potentially saintly body with the stresses of the bureaucratic processes of the church paints a funny picture of the world:
...he delivered a letter almost sixty pages long to the Secretariat of State but received no reply. He had foreseen this, for the functionary who accepted his handwritten letter with all due formality did not deign to give more than an official glance at the dead girl, and the clerks passing by looked at her with no interest at all.
One of the most interesting things I find about this magical realism is that, at certain times, I am unsure whether the story is real or entirely imagined: would they really eat songbird stew together? It's not as magical as a dead girl who resists decomposition, but it's nonetheless a foreign idea to me (although altogether possible). (I feel the same way about science fiction sometimes - it's interesting because it inhabits the line between reality and fantasy... e.g. Jurassic Park's very dry, "historical" introduction by Michael Crichton.)
I got tingles at the end of the story. It jumped up on me all unexpected.