Why not just "steal" an M-14 from a National Guard armory? You can frame Oswald for that one too, and you have a .762 weapon that's capable of full-auto, and had a 20-round magazine. He could have killed everybody in the President's car, the second car, and even LBJ's car. Go big or go home, right? With five magazines he could have shot it out with DPD for a while and gone out a legend.
Either way, if I'm throwing an assassination in 1963 I'm arming my shooter(s) with M-14s because it widens my pool of applicants to every man with prior military service, it's an easy weapon to get your hands on if you're an evil shadow government type, and it's more reliable than the Carcano while being harder to trace (unless it's left at the crime scene, and even then it just gets tracked back to the NG armory we stole it from).
But that's just me.