I had a .308 that shot just like that. The problem was a crooked chamber. The temporary fix was to FL size the cases, and Jam the bullet .010 into the rifling, which is ok at the range but will likely cause problems in the field.

If you try this and it shoots the same groups repeatedly, even if they are around 1", it might be livable until you can get it rebarreled. This won't cost you anything but a trip to the range to try.

"Give a lazy man the toughest job, and he will find the easiest way to do it"