"...the 7.7mm Jap is the .303 British..." No, it isn't. Different case altogether. Especially the rimless part of the 7.7 Jap. Only similarity is the bullet diameter.
http://stevespages.com/jpg/cd77x58japanesearisaka.jpg
http://stevespages.com/jpg/cd303british.jpg
Norma loads 7.7 Jap. So does Precision Cartridge(Graf's) and XCaliber(via Ammoseek). All are using hunting bullets. Prvi makes the brass. Hornady only makes it in their custom shop and not regularly. Isn't listed on their site at all.