Re: Bullet runout?
One way to improve TIR is to use an expander before you size. (Not the expander ball in some dies.) Sinclair and K&M sell them. Then size with a good bushing die. The shell holder must be correct also.
Straight neck is critical. As for straightening them out with a tool afterwards, I have heard that it can be done, but the next loading will again not be concentric and the same process must be repeated. Your seater die can be to blame also. The tip of the bullet can touch the seating dome inside the die, and skewer the bullet to the side.
The very best bet is to use Wilson dies with an Arbor press and you should have no problems.