I hesitate to press the point against people who know much more about this than I do, but I'm looking at it as a lawyer, construing the words used, rather than as a scholar with knowledge of his oeuvre and his method of working.
I certainly agree that there is no confirmation she has died, but that suspicion would be rife. But surely if the whipoorwills only appear in the immediate vicinity of the dying, the immediate reaction of the other folk should be "There were whippoorwills up at the Whateley house. Which of the Whatelys has died?" So the line "None of the country folk..." should rather read "None of the Whateleys was confirmed dead, but...".
I think that in part yes, it's the literalism which is getting in the way here, as Lovecraft (as was his wont) is blending several approaches throughout the tale: the formal, erudite third-person narrative voice; the scholarly but pedantic and at times ponderous and even foolish views of Armitage, whether in direct monologue or compressions or redactions of his thoughts; and a narrative voice which approaches a condensation of the confused, uneducated, and frightened mindset of the countryfolk of Dunwich and its surroundings... people who, it is hinted, are descendants of actual witches (having fled from Salem at the time of the witch scare) and living in a region where the actual presence of the past heavily outweighs that of the present, both physically and mentally. (Physically, the newest building was constructed very early in the nineteenth century; mentally its presence is reflected by their archaic dialect, which reflects something very close to the country dialects of the Puritan era and shortly after, as recorded by James Russell Lowell in
The Biglow Papers.)
Thus what we have here is not entirely an objective observation, but something which blends an objective narrative voice with the reactions of the Dunwich residents. Such often tend to think less logically on such matters, and often begin with a more general idea of "who in the area (of Dunwich) had died" before going on to make the connection with Lavinia or the family of Old Whateley. Even then, though they would suspect, without confirmation they would not be prepared to voice such suspicions directly (very much a Yankee reservation of the period there), for fear of both the involvement of the law (outsiders; seldom welcome in such a furtive community) as well as the implied moral burden of confronting such a character as Wilbur himself for either confirmation or censure (the last, of course, being entirely unsafe, given his predilections naturally and supernaturally).
This being the case, the phrasing, I think, would be intended to reflect this conflict of viewpoints, concerns, and reticences....
That was certainly the inference I had drawn, until I started wondering about this. As a matter of interest, are the whippoorwills referred to in other stories? What would happen if, say, a person had a heart attack while tending the cattle outside?
No, he never used the whippoorwills again in this way that I can recall. This reflects the fact that this was an actual traditional folkbelief of the very real region upon which Dunwich and its surroundings was based, as I mentioned earlier. Another such blending of genuine lore or fact is his reference to the fireflies who "come out in abnormal profusion to dance to the raucous, creepily insistent rhythms of stridently piping bullfrogs". This is his use of something he himself encountered while in the Wilbraham area. As Joshi mentions in his note (in The Annotated Lovecraft):
Lovecraft saw an "absolutely marvellous firefly display ... All agree that it was unprecedented, even for Wilbraham. Level fields & woodland aisles were alive with dancing lights, till all the night seemed one restless constellation of nervous witch-fire. They leaped in the meadows, & under the spectral old oaks at the bend of the road. They danced tumultously in the swampy hollow, & held witches' sabbaths beneath the gnarled, ancient trees of the orchard"
This is from a letter to his aunt Lillian D Clark, of 1 July 1928.
As for the last question -- I think we see something of this with the "death" (or dispersal) of Wilbur's brother, who meets his nemesis atop Sentinel Hill. There, the whippoorwills surround the entire area (a hint, perhaps, that the number of whippoorwills would be related to the "size" or strength of the "soul" in question?), so much so that, when blasted with the being's "demise", "over field and forest were scattered the bodies of dead whippoorwills". (Obviously, Wilbur's brother's "soul" was nowhere nearly as human as was his own... which merely caused them to flee in panic.)
But could they not have augmented the usual ritual by killing her in some way?
I'm not sure what you mean by "augmented" here... but it is quite possible that she was offered up as a sacrifice by Wilbur magically... whether any actual physical violence on his part was a part of it or not. This is a point which is left obscure, I think, to deliberately increase the reader's disquieting sense of unease about exactly what did happen to poor Lavinia....