Bravo! Good thinking! 
"Quotative inversion"? 
Sorry, but I think that's funny. 
I wish Mary Norris, the aforementioned
New Yorker proofreader who has written a book and a bunch of articles and I think even has a TED talk, would address the subject. I looked her book up on Google Books and searched "quotes" and other possible references, but nada.
Yet at some point it must have come up. It's the weirdest thing the
New Yorker does. There is widespread distaste for this practice outside the magazine, but nobody seems to know whether it's an actual ban and, if so, why. Why would they refuse so stubbornly to adopt a style that isn't grammatically incorrect and reads much more smoothly?