What a bad story and what a nice episode about it.
Although the story is not well written with respect to plot, conflict, tense, meaning, etc. it truly is a Le Fanu story: his writing style, his putting down words, is very recognizable.
I picked Le Fanu's collection of tales 'In a Glass Darkly' two years ago as a book to read by my own book club (we only read world classics). I already heard of 'Carmilla', but when I read the whole collection, many tales immediately became one of my favorites ever (in particular 'Green Tea' and 'The Room in the Dragon Volant' - the former a really good Victorian weird tale, the latter an interesting Victorian mystery, both full of plot and good use of storytelling techniques).
I mention this, because there HAS to be a reason why Le Fanu wrote an Authentic Narrative as it is. I agree it probably has to do with being it some sort of writing experiment (with a really not satisfying outcome).
In the collection 'In a Glass Darkly', Le Fanu uses a frame story to fuse the stories together. The way in which he did this also really didn't work. The stories, he tells the reader, are cases of a psychiatrist (like the events in An Authentic Narrative is a bare list of unexplained happenings); they should clarify how he resolved/explained the strange things happened to his patients - which he absolutely does not. Maybe this also was a satire on aristocracy or maybe psychiatry, who knows?
What IS interesting in this frame story is that Le Fanu uses the psychiatrist to tell us about the theories of Emanuel Swedenborg, the famous 18th century mystic, who posited a so called Swedenborgian Space, the realm between the living (body) and the dead (soul). It greatly influenced the spiritist movement and ghost stories in Le Fanu's time, and I believe Le Fanu himself was an advocate of it. Although An Authentic Narrative is almost too much rationalist, Le Fanu leaves all this explanatory Swedenborgian stuff out of it. It cannot be otherwise: Le Fanu must have left all this sort of things out of the tale on purpose.
But I can’t explain why – it's a real mystery. Weird. ;-)