I wouldn’t call it a “step-up”, more a focusing of production on just the .38 M&P model in both calibers. I do not know, however, when the respective last “pre-war” specimen of other revolver models were built and shipped.

Roy gives 670,000 as the approximate beginning of BSR production. As an example, I have made note of 676761, a .38 S&W shipping in 01/1940. The .38 Special version was first shipped to the military in a large batch with the Navy order for the USNCPC in spring 1941, still in commercial configuration except for the swivel.