Using Michael Wright's Guitar Stories Vol. 2 as a reference, a photo of a Rex Aragon with the deluxe style headstock is shown on page 112. Wright dates this one to 1948. Gretsch made the Rex brand during the 20's 30's, and Kay may have distributed some of them. (Remember Kay was a huge distributor with contracts with Montgomery Ward and Tonk Brothers). Kay made a lot of instruments in Chicago and out-sourced more to meet demand. I have a "Kay Superb" archtop with the deluxe style headstock. My best guess is that this was a transitional piece post 1938 when Gretsch discontinued supplying Kay, maybe post 1948, the date Wright attributes to his deluxe Rex Aragon. At about that time, Kay embarked on making and selling the post-war "Artist" series of archtops.

I'm not sure how all this washes out. Perhaps Kay picked up the Rex brand after Gretsch quit building them, then added the Aragon to differentiate and make it a higher end model. But then with the introduction of the "Artist" series around 1948 Rex Aragon was redundant. My best guess.