Generally speaking, and I mean generally, the Arisaka Type 38 action is considered to be one of the strongest ever put into a military bolt action rifle.
I say generally because some of the late war guns were breath-takingly horrible.
Type 38s, and 99s, as well, have been converted to a lot of different calibers over the years, with varying amounts of success. One of the most common was 6.5x257.
Head and rim diameter is actually quite a bit different according to my books -- .455 for the Arisaka to .466 for the .308. Rim diameter is similarly different.
Believe it or not, the .30-40 Krag is actually a LOT closer to the size of the 6.5 Arisaka. Perhaps you could have someone chuck some .30-40s into a lathe and trim the rim for you.
Another possibility is the .35 Remington, but the case is a bit on the short side.
Maybe, in the long run, the best thing in would be for you to retire the Arisaka and get youself a 6.5x55 Swede, and work it over. Another great cartridge.