I take HS besides the serial number 135 as the initials of the real maker. Flintenkalle’s Directory has only 5 Austrian gunsmithes with those initials. As Herbert Scheiring would have used his Ferlach “house number” and 3 others were close to Ferlach, I would bet my money on Helmut Srugger in Gmunden. As a family tradition seems to point to a gunshop in Bad Goisern, a maker in nearby Gmunden is likely.
For registration purposes I would simply name Srugger as the maker, identified by his initials HS. Who could ever prove otherwise? Here in Germany countless prewar drillings are registered with “Suhl” or “Krupp” and any bolt actions wih “Mauser”as the maker.