Not sure how you'd chamber and fire a .30-06 cartridge in a 7.7 Jap, but using the brass to trim and reform into the Jap caliber is something I often do to keep costs down. You can even use other cases in the '06 family, such as .270 Win and .25-06, but they're more difficult. 8 X 57 Mauser's another good one.
I haven't had any problems with short case life due to base bulge, but neck splits can happen if you don't anneal the necks.
Sportsman's Guide often has 7.7 Jap in Norma, Hornady and possibly other makes. Not cheap though. Reloading's your best bet. You can also use .303 Brit and 7.62 X 54R projectiles in your 7.7 reloads. They're all .311, so they're a pretty good match for the Arisaka.