Hello GG,
Are you sure the stock is stamped "Vienna", not Wien or Vienne?
What is the serial number of the rifle? Is there a different number inside stock?
In the time period indicated the main distributor/dealer for the Steyr hunting arms was Johann Springer's Erben Wien (the other was Nowotny Prague); so this could be the maker/provider of the custom stock. Springer's still keep the old records.
Since the Steyr Gun Room decorated by Russian POWs during WWI is still preserved in the factory I would say there is good chance the old records are in existance, somewhere. As Raimey says, Mr Felix Neuberger should know more about the fate of the Steyr archives.
With kind regards,
Jani