Indeed, British gunmakers did customize and 'have their way' with some M1900. They were essentially prototypes to begin with and and Paradox's is a very low numbered example.

Here's a Gibbs M1900 with a takedown stock of a very different system than that of the Steyr built sporters:

The 'factory' version as used on M1903, M1905, M1908, M1910:

Notice the "Horn cap at the muzzle of sporter type" available from the options list. By 1939 (date of these Stoeger catalog images) there were also 'three leaf express sights' available, at least on the 'High Velocity' (A.K.A. M1925). Paradox's stock does appear different from the 'factory' MS stock of the M1903 through M1910, though.

What I've never seen before is this, which amounts to Osterr. Waffenfabr. Ges-Steyr in English.

That's quite a find, and may lead me to suspect that the action was originally made for a sales sample to be 'shopped' to Britain or the United States in effort to acquire a military contract. That is what M1900s were all about and did result in the Y1903 through 1930 'Greek' models.

Could this be an 'American Eagle Luger' of MS rifles? It would be interesting to know when Dickson & Son did their work on it and for whom.

I did just find a reference from the Great Britain Patent Office Commissioner of Patents' Journal of 1879 where a patent was granted to the "Austrian Small - arms Manufactory, of Steyr [sic]". Perhaps this action was from a rifle submitted for a later British patent?