According to Jim Cate's book "J.P.SAUER & SOHN" the 182681 serial number is datable to 1911-12 also. S&S serial numbers are of limited use for dating, as they were given at the start of the making. Some S&S guns then remained in stock for several years in some state of manufacture until an order came in. Such guns were proofed and finished only then.
The rifle was certainly made for Export to the USA in the first place: Before WW2 the .30-06 was about as popular in Germany as metric numbers were in America, in short: unknown as a hunting number. The "Prussia" or "Made in Prussia" address is found on many Sauer & Sohn guns imported by Charles Daly pre-WW1. It was meant to distinguish the "superior" Suhl made guns from the "inferior" Zella-Mehlis made stuff. Suhl was in Prussia, but nearby Zella-Mehlis was part of another German state, the Duchy of Saxe-Coburg-Gotha.