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Did you check the run out on the loads that someone else loaded for you?
If they are around the same as yours then run out is not your problem. As stated in other replies its more likely you are not...

4 Thou runout is pretty good for standard die sets but 5.5 - 6 thou for the sierra's is not so good, they look like quite a pointy bullet so I am betting that the seating steam does not match the...