Triple Deuce: Just for your own peace of mind, load the brass with the worst runout identically with an equal number with the least runout, take them to the range and shoot for group size, side-by-side. Bet you will see very little, if any difference, especially at 100 yards, and doubt at 200 yards either.
Actually .003" of total indicated runout is not bad in my book, more than that and I would agree it would start to be a concern, but at the shorter distances that the 222 is capable of, I've never seen it as a problem.
I also believe in seating the bullets incrementally, seat 1/3, rotate case 120 degrees, seat 1/3, repeat for final seating. I'm also one who believes that occassional runout is caused by a piece of defective brass, otherwise all 20 would have equally bad runout, as opposed to the usual 1 or 2 rounds that I may get out of 20 loaded. Minimal, or no runout with 222 Lapua brass, just a little more with Winchester, but not enough for me to worry about.
Using the Sinclair dial indicator concentricity gauge to check for R/O.