Redding makes competition die sets that come with a collet neck sizer, a full length die, and a precision seater die. It will probably solve the run-out issue but they are expensive. I have a set I use with a 300 WSM and run-out is always between almost .000 and .002. With the majority at .001. The rifle usually shoots between .5 and .6 MOA.
I think a big question though is if your rifle will shoot any better with lower run-out. The run-out gauge I use says that best accuracy is achieved with less than .003 run-out, but I have never tested it. Why not group some of your loadings above and test the results. Group a bunch of the .008 and .009s and the .003s with the .004s and see if there is a difference in accuracy? Then consider going with the more expensive die sets. I would be interested in your results.