The thing has lot of charm going for it, and .264Mag goes quite well with a Winnie action made up into rifle at that time. I have handled old .264 Winchester from the same period and they are not in the same league. The caliber is a bit obscure, but one can still find ample supply of 140grainers from Remington in bigger gun shops plus it's just as good as .270Win, 7x64, 6.5x55,....
Italian, have you tried 3-piece aluminium rod from the muzzle end? It will do "wonders" for them groups!