I've converted -06 cases (.270, 30.06 etc) into 8mm Mauser. Just have to run it through the sizer, trim, run it through the sizer again, check length, trim/size as necessary until it's the right length.
According to my conversion chart, 7.7x58mm Arisaka, can be converted from -06 cases. So, it should be the same process. Just be aware that since the -06 cases are 63mm long instead of 58mm, you won't be able to size it all the first time. Just go until it gives firm resistance. Lube the cases well too.