While I continue to investigate, I see that Wikipedia states the European designation for the .22 Hornet as 5.6 x 35R (not 36R) and credits Barnes' Cartridges of the World (which I don't have). Probably a mistake and just an example of how these things seem to always drift further off course.

I also found a 1938 DMW ammo catalogue online: http://gigconceptsinc.com/files/DWM-1938-Export-Catalog-tan-brown-cvr.pdf

On page 14 of 44 the Vierling is pictured just above the Hornet.

Would love to run across a case of the Vierling ammo! I'd also like to know the last year the cartridge was loaded by any of the major companies.

I think it might be worthwhile to look at some of the writing on the Hornet around the time of its introduction (1930 according to what I've read). Surely they must have compared/contrasted it with the Vierling.