Re-reading and some more time to reflect, we have to make a lot of assumptions regarding this mating. The stock has been mated to three rifles, two other prior to yours, the "BS" on the stock could have been a prior mating (and not connected to this receiver), 7349 was probably the first rifle. The barrel is factory original, obviously the intertwined BS on the RR represents its own connection to this mysterious "BS" relationship, but it is a stretch to make wide sweeping connections/observations on a rifle that has a stock connected to 3 rifle mating's.
The wrist markings might be helpful in the sense it could date the last rework, if it was late, say after the mid-1920's, it should be more regimented, strictly organized to what we are more familiar with (Wehrkreis districts/ordnance shops), if it is earlier, closer to a more chaotic time (1918-1924, or pre-1927 anyway) it may just add confusion (hopefully the "last" visit can be identified by the wrist). The early republican period there only officially existed two ordnance shops, one at Berlin-Spandau and the other at Cassel/Kassel, these two HQ controlled the existing Reichsheer and had ordnance operations (both technically illegal), this is "probably" where the B.S. comes in, - looking over my trends and drafts (article projects) my thoughts were these "BS" markings could have been an early form of ordnance acceptance, the weakness in that theory is the Cassel/Kassel acceptance always followed a more formal/traditional pattern we are all familiar with and the question arises to why Berlin-Spandau didn't? Berlin-Spandau would have been the higher authority, one would think, and set the standards Cassel would follow... Perhaps, these early BS marking represent an earlier acceptance before the more formal standards were applied, perhaps before Cassel started inspecting or reworking rifles.
With Cassel/Kassel it is easier to date the work by acceptance patterns, "Eagle/Cl" obviously dates to before 1926 when the city changed the name from Cassel to Kassel, then changing the ordnance acceptance to "Eagle/Ka" sometime after 1926, this process probably took time, probably a couple years after 1926. This intertwined "BS" may have been a very early form of acceptance, before more formal acceptance patterns were established, the latter "B.S." being part of the evolution, eventually changing to "E/Su" we are all more familiar with. Later both ordnance shops would add numerals, probably representing individual inspectors or shops.
One thing is for sure, all this is guessing, mostly based upon existing trends and everyone knows the rarest rifles 1914-1945 are period original matching republican era rifles, and even among those that exist they fall into the same category as yours. They have been through several repairs or inspections and it is difficult to connect parts to these visits or periods. Worse, of the three eras that divide modern German military history (Imperial, republican, national socialist) the least written about is the republican era, especially in regards to its military structure. Most books that tackle the subject in English focus upon the military's role meddling in politics and the extent this led to national socialism (which is a stretch, - many of the authors are social democrats, sometimes former communists, and are hardly objective in their analysis, forgetting that the communists were the ones who refused to work with the social democrats/SPD against Hitler, and even voted with the nazis against the SPD, not to mention joined the nazis in riots to topple the government... nazis and communists are Kane & Abel of ideologies, ideological brothers that tried to kill one another for the god of power. )
*** BTW, this is the highest Amberg/1910 known, not a large jump, about 100 rifles, interestingly, the one it replaced as high was 6219/a
Also, I am moving this to the interwar forum due to its important connection to interwar reworks..
