I'm not sure the case is closed on this one. Somehow, Edith Fowke knew that the person who had copied the song from Sara A. Price's diary was Keith Clark, recreation director of Ottawa, Illinois.

Keith Clark recorded an album for Folkways of songs he wrote about the history of his county. One of the songs is about Willy Price, who was killed in the Civil War, and whose brother was also killed in the Civil War, and who left a diary behind. Keith gives the name of the man who then owned the diary as John Wilson. You can see all that here

Edith Fowke generally didn't make stuff up. Keith Clark was famous for chasing down old diaries. It certainly sounds like Keith Clark might have actually encountered the diary of Willy's mother, and found "The Housewife's Lament" inside. Sadly, we have no date for this diary--it could easily have been pasted or written in after 1871, making it simply a single copy of an already-published song. But the story itself, about it being found in Mrs. Price's diary, seems plausible.

It occurs to me that if the song appears in the collected reprints from Sing Out, it must have appeared first in an original issue of the magazine. Perhaps they condensed the notes for the reprint, and Keith Clark contributed it to the magazine originally with a longer note. That would explain how Edith had his name in connection with it. I'm away from the Library for a week, but I'll try to check when I get back.

Also, a Q notes above, The Housekeeper's Woes, a 5-stanza text attributed to H. A. Fletcher, appeared in the It's Naughty but It's Nice Songster of 1871. That means the earliest published version with a name on it had Fletcher's name, not Turner's. I'm not sure why folks seem to have concluded that Turner is the author.