This is, in fact, a 1913 DWM military, late model in the "b" block, WITH stock lug.
According to Jan Still’s “Imperial Lugers” page 23,
“There was a transition period during 1913, when changing to a hold-open and the addition of a stock lug. . . . . . . . Although the stock lug is found on some of the last production 1913-dated Lugers, it is lacking on some early production 1914-dated Lugers.”
In "Imperial Lugers" the picture on page 39 shows an example of this type Luger. It is a 1913 WITH a stock lug and a serial number, 5486b. Note the "b" suffix.
I own a 1913 DWM in the "b" block; it has a stock lug; and is identical to the Simpson D-44 except for serial number.
It appears that there is nothing about the current Simpson listing (D-44) to indicate that it is a commercial Luger.