Here's a thread (from a noteworthy and admirable 'site) about M1900 serial #295:

NitroExpress

It was Austrian proofed in 1901, but later suffered a rebore and an alphabet salad of stampings that Kuduae sorted out.

Here's M1900, #198 - rebored and Nazified: M1900 #198

And the thread about your own amazing #373: M1900 #373

It seems that these informative threads and the responses therein (combined with other information) point to origins of several M1900 examples as having been originally built for military trials with several having been reworked to various extent afterward. That would seem to account for examples of M1900 actions, manufactured in Austria by Steyr, with British, Belgian, or other proofs while lacking Austrian proofs. The 'Modell 1900', "Austrian Small-Arms Manufactory Steyr", and other stampings found on some examples reinforce.