I no longer own or shoot milsurp Carcanos.
Not because I don't like them, because I do.
I'm one of the few people here that's been able to compare the Type I Japanese Carcano, chambered for the 6.5 Jap, against the Italian issue Carcano, chambered for the 6.5jap.
I had three of the Italian made Type I Carcanos, and several of the Italian Carcanos. The only real difference was the Type I rifles had a swing flooplate/triggerguard and an internal magazine, rather than the Italian enbloc system.
I was a bit surprised to find the Japanese and Italian bore diameters were within a few thousandths of each other, between all of the rifles.
You're likely onto something about the jacket material, but IMHO, the real difference was the "exposed lead bases" in the original Italian and Japanese ammunition, along with faster powders of the time, which enabled the jackets to be forced into the grooves better than powders/bullets available today.
I have a bunch of milsurp cupro-nickel 160 grain RN, exposed lead base bullets made for the 6.5 Swede.
These shot acceptably in all of the rifles, but not quite as good as the Hornady .268 solid base.
Hornady solved the problem that exists today, by making bullets to properly match the the bore specs of the Carcanos, and many 6.5 Jap chambered rifles.