Please excuse my ignorance, does this rifle have a plunger type ejector?
If so, when a bullet is seated so that it is very close to the lands, and the cases are unfired or FL sized, the cartridge can be pushed to the opposite side of the plunger and the end result is contact on one side with the rifling, although it may look like a crooked chamber or throat it most likely isn't in the presence of a plunger type ejector. If the rifle doesn't have a plunger ejector, then I would have a chamber cast made to assess what the cause is.
Do your fired cases show any signs of chips or the like in the chamber?
Is it possible that a partial ring of bullet jacket material is stuck in the throat and forcing the cartridges to one side?
Have you cleaned the rifle since finding this problem?
Hope this helps you out.