My spider-sense says this is like those economic or political crypto-readings of The Wizard of Oz
that marshal a lot of seemingly significant coincident details in the service of an over-developed conspiracy theory that is hard to refute but which completely misrepresents the real genesis of the story.
Some perspective: The story's origins are semi-autobiographical. Miyazaki's mother was hospitalized with tuberculosis when he was a boy, and his father brought him to the country. His mother was hospitalized for years but eventually left the hospital and lived at home with the disease for years. She did not die in the hospital.
For the film Miyazaki decided to make the protagonist a girl rather than a boy, and later split the girl into two girls (with essentially synonymous names of Mei and Satsuke, both of which mean "May"). The idea that they were inspired by the two girls in the murder case is false.
The theory that the soot sprites are heralds of death is contradicted by the fact that the old lady neighbor saw them too when she was a girl, and makes it clear that they're visible to children rather than adults.
The claim that toward the end of the film the girls have no shadows is false
The theory that the sandal Satsuke denies is Mei's is actually hers is false. Mei's sandals are close-toed, the one in the water is open-toed.
A number of claims, such as the specific mission of the gods represented by the six statues, are unconvincing. I would want expert testimony before buying into that, and I bet expert testimony would rebut the idea.
Attempts to explain away the end credits, which clearly show the further adventures of the Kusakabe family after the mother's return from the hospital, are wholly unconvincing.
FWIW, there's a sequel short called "Mei and the Kitten Bus." Both in the beginning and the end Mei is living at the Kusakabe house.