I don't have info on every year by a long shot. It's been in May for over 2 decades now (when I started taping), and even before that, when I'd catch the show on a dorm TV or whatever, the telecast was always in the spring, with a cutoff date a month before. The very first awards were presented on April 6, 1947. I found an old news story on line about the producer of Hair bringing charges because the cutoff date (in 1968) was changed from April 10 to April 3 to March 19.
At that time, the cutoff was a month or two earlier than it is now, and shows at the end of a season frequently weren't eligible till a year later. So there has been some variation over the years. So... I suppose we could say that in the fictional year covered by this book, they switched it to December 31.