[tom hyle]

Japan, most obviously. European and Afrasian cultures seem to often have edge-up carry as an occasional option, often seeming idiosincratic, but IMHO an ancient an long enduring but just rarely poplular custom. The Germanic saex was often/usually worn edge-upwards. Traditionally in Europe Military commanders would often have their men dress or arm after their own (the commander's) idiosyncrasies, especially as to weapon selection, sharpening, loading details, etc.
Edge-up carrying keeps the edge from wearing against the sheath and getting dulled.
I salute your cutling ambitions, Sidney.