"Deluxe '31? I see a step plate for the Rumble Seat, and a chrome windshield frame...."
Could be. The stainless steel windshield posts seem to be the right height versus Standard Roadster posts, which are taller. The cowl lights are another possible DeLuxe identifier, although many Standards received them from owners or dealers, akin to rumble seat additions post-factory. The windshield frame itself would have been chrome plated. But after years of exposure in this environment, the plating would have certainly gone away, resulting in the frame looking like it does here.
The odds are also in favor of this being a Deluxe Roadster. According to the DeAngelis book, there were only 5,499 Standard Roadsters produced in 1931, while the DeLuxes reached a whopping 52,997. That equates to about 10 times as many Deluxe Roadsters that year than Standards. Why wouldn't anyone back in the day pay an extra $45 or so to upgrade from a Standard Roadster to a DeLuxe, considering all the extras one got with the DeLuxe model? Yes, $45 was actually $45 back then and a hefty chunk of change during the Great Depression. But what a difference between the two models for a measly $45 Yankee cartwheels!
Marshall