Re: Run out
Tim, If I had to guess, I'd say your using RCBS dies. They are notorious for being out of round. Most of the guys at the 1000yd range avoid them like the plague.
Assuming that is wrong, you may have a chamber that is "Banana'ed" It kinda had a curl to it. All of your fired rounds will pick up the chamber shape to some extent. Some might be the same orientation (rotation)as last firing and now their worse, others might be opposite that and now they get better.
Spend some time checking the brass before you resize, and after. Move your indicator to the center of the case body and support the case on the mouth and head at the same time. Now check. Keep in mind, double the result when you check the bullet runout because it's outside the supports instead of inside. Your .006 runout on the bullet means its really .003 off center.
Hmmm, now to really answer the question, is .006 bad. For ME, yes, on my match gun. Would I be afraid to shoot at a woodchuck at 400yds with a 22cal and ammo that measured that, No. Would I be surprised if I missed, (with a good range) Yes.
Most of all, Don't think that it's You. There's nothing you are doing to cause that amount of essentricity. Your gun or your dies are hosing you. For <$25 you can find out if it's the dies. Get a Redding FL die and see if it fixes it.
Be happy with .001 or .002 on the bullets. You'll grow old trying to get much better than that.
If you have something that you disassemble and reassemble enough times, sooner or later, you'll have two!