These are very fine angles, I doubt you missed something important... The exact definition of the unit I would have to access my library, but probably police of one fashion or another, - Germany had police forces that would boggle the mind prior to 9/11, today the early German republic look modest in its creating police variations, but at the time seemed excessive (they had train robbers to river pirates).
Besides the bolt it is a fine example, some graffiti but fairly modest to many from this period, barrel is original (Police had their own ordnance facilities and it is common to see their work, especially barrel replacement (again I assume this is police) but it certainly is lacking typical police alterations - they typically have a number of modifications or alterations as the police were very busy 1919-1933... I will check the unit marking in books when I get a chance but there is a good chance it isn't because it is so original to its original state- only TD added to an otherwise factory stock- might look to the disc for whom added it, originally this rifle had neither grips or the TD, this is a fact... far too early for either)
Honestly I have doubts this is police but I would have to refer to books in this regard as my specialty is more on the rifles, trends, mfg's and historical context than unit markings.
*** I really didn't think this rifle very interesting, but is rather exceptional (the original stock especially), makes one wonder how many other quality examples are discounted by poor initial pictures, - nice rifle!