Tom,
You might want to shop around a bit on the Redding dies, unless you're talking about the three die Competition set.
For way less expensive, give the Lee Collet die set a look, it works quite well.
The runout may come when you seat the bullet, try seating it 1/2 way, rotate 90*, and finish.
If you have an increase in runout after sizing, the expander ball is very likely yanking the neck out of kilter. The bushing or the Collet die will obviate this. Polishing the expander ball to a mirror finish helps, as does lubing inside the neck.
Just some thoughts, hope they help...
Tom