the "M" throws me. It appears to match the 1920 commercial in all other regards, but a quick trip through the Standard Catalog of Luger and I couldn't find that specific cursive "M" anywhere (although I'm positive I've seen it somewhere before).
The closest I could find was that exact cursive "M", but with the letter "A" partially entwined below the M. This is listed as a marine arsenal acceptance mark. And it has no business on a .30 Luger.
A little further reading indicates that the "M" might signify the pistol was reworked by Mauser, but that is speculation, and wouldn't be "right" for a .30 Luger, either.
The 1920 Commercial should have "made in Germany" or "Germany" marked on the frame, however it appears that some were not marked.
You need a real Luger guru for this one, I think. One thing mentioned in the book, its those little markings that make the difference between a common Luger and a really rare one, or as the author put it "between a $500 pistol and a $50,000 one"...
Commercial proof, ok. .30 Luger, ok. Not frame marked ? apparently ok. But the "M"? its beyond my reference material. Sorry, you need someone more expert than I to ID that one.
All else being equal (and it almost never is) bigger bullets tend to work better.