The 135mm lens was introduced because it was the longest focal length that could be accurately focused with the Leica's rangefinder. And that it was already a common focal length for 3x4", 9x12cm, and 4x5" cameras.
Remember that telephoto lenses (on any cameras) were extremely rare before that time, so a 135mm lens was an amazing advance in capability- that did a great deal to sell Leicas, Contaxes, and their later competitors.
As far as the OP's question about differing results with different camera models, no. There has been no evidence (in the last 70 years) that there is any image quality difference between any of the Leica M camera bodies. Of course you may think so, and if you set out to prove it, you'll likely find it; that is what's known as "confirmation bias". Or less politely, "bat***t crazy". What follows from that (as we all have learned, sadly) is a conspiracy theory, "There is a difference, but THEY are all covering it up".
You might as well look for image-quality differences between chrome-plated and black camera bodies. Oh, and show your results, please!