Really good pictures!
Well it is certainly a sterngewehr, and in the same pattern as all the other "Simson" marked examples, except for the lacking "star". It has the exact style of acceptance, the tg has the suffix, the style of the fireproof etc..
A collector in Germany has a rifle very close to yours, about 1200 rifles before yours, his rifle is much the same and his stock is Saxon cyphered, as are all the others with an original stock.
Weird part, is these "Dresden" sterngewehrs with Simson receivers do not share a similar RR acceptance pattern with the other maker marked rifles (Spandau's) but largely are the same otherwise. These Simson "sterngewehrs" do however all share a unique RR acceptance, slight variations but consistent, - it is different than normal Simson production and from other that are attributed to Dresden.
Not sure what this means, - whether they were made at Simson, Dresden, or something else. Only that they share many characteristics of rifles I attribute to Dresden but they have a unique acceptance pattern.
You did well for $300 getting a Simson matching action. Simson marked (sterngewehr or regular production) rifles are very elusive in any decent condition. Easily the scarcest manufacturer represented in the database.
A lot of bargains were had at that auction. Did you happen to catch who bought the depot marked 1918/28 VCS? It had a “Zn” across the top?
Now that was an interesting (and important) rifle!