Interesting that you gathered that much solid info from these images.
You may want to look into what H. Krieghoff Waffenfabrik was actually doing prior to the contract for 10,000 P.08's.
The 10,000 are not reworks.
I think the point is that "H. Kreighoff Waffenfabrik" and "Sempert & Kreighoff" were the same company. S&K was just the brand name Krieghoff stamped on its sporting guns. Same company, same factory, same people, though its possible they may have remained legally distinct for tax purposes or liability or whatever.
Here are some period drawings of the S&K factory from a 1927 catalog, and the Waffenfabrik from probably sometime in the 1930s. Same complex.
You may want to look into the "Model 1934 Sporting Rifle" and how the contract was passed from H. Krieghoff Waffenfabrik to S&K.
That the 10,000 P.08's contract was awarded to H. Krieghoff Waffenfabrik is likely true.
That it was their first contract to produce new arms for the German Military is likely true.
I would think some of our German members could carry that further.
That the S&K firm was deeply involved in the production- finishing speaks for itself.
My opinion on that is based on the comparison of 1937 to 1937, 1940 to 1940 etc.
If you are looking at honest examples, it will be obvious.
The 10,000 contract was only a way into Military contracts.