Brad,
That is actually an interesting variation. A couple of years back, I picked up one with that type grip that was about NIB- # 384359, shipped Oct, 23. I had not seen one with the Reg Police type grip before that I could recall, so I queried Roy about it.
He said that when they got back into production after WW I, they tried to simplify inventory by using the Reg Police grip which had been designed in 1917 to give a larger, square butt grip to the 32 HE frame. Earlier Bekearts had the larger, oversize grips that filled in behind and below the grip frame of the 32 HE frame when used on the 22/32. Apparently, the public was not thrilled with the smaller grips like those, and S&W went back to producing Beakearts with the unstepped backstrap and the larger grips.
That means a Bekearts can be found with at LEAST 4 grip variations in chrono order-
1- Large, extended grips with Gold Meds: 1911 to WW I
2- The Regulation Police style with no meds: Post WW I to 1924-25???
3- Large, extended again, but with no meds: 1924-25?? to 1929-30
4- Large, extended, with silver meds: 1929-30 to 1940-41, and Post WW II to 1952-53??
#2 above is the only one that should have the stepped backstrap. I don't think that style made it past 1924-25, due to public demand for the larger grips. I have observed more with the large, extended grips without meds than that Reg Pol style. I think customers who had seen a friend's earlier gun with large grips, and then ordered one, was very disappointed when it came in with grips sized to fit his little girl!