First of all a standard sizer squeezes the case neck down way below bullet size...

THEN...dragging an expander ball through a small neck ALWAYS squirrels things up no matter WHAT you do unless you start with measuring your chamber neck and chamber...then match the sizer to fit with a minimum amount of squish and take that expander ball and use it for a fishing weight. The only expander balls I use are NOT BALLS, they are elliptical shaped or tapered rods...and unless you clean/polish the inside of EACH case neck with a bit of steel wool on a brush running in a drill motor AND use Imperial wax on another brush to slick up the neck inside, or dry lube, you will keep spinning your tires...FOREVER.

The BEST thing you can do is to buy a Redding or Wilson FL bushing type die...measure a fired case OR better yet have a chamber cast made so you know, exactly, the neck OD...THEN buy a bushing that reduces the neck ID 2-3 thou smaller.

Go to a benchrest forum and read how those boys do their case and follow suit. You don't have a benchrester but what they do to their cases is part and parcle of those small groups they shoot.

You are already working with a factory chamber unless you had the rifle custon built and can get the dimensions from the reamer that was used to cut the chamber...which means you're chasing after butterfly's...no diss or flame intended...I did the very same things 50-60 years ago.

You need to FL size your cases with the sizer screwed down 1.5 turns past where it hits the top of the shell holder at full stroke...NO BREAK OVER...a solid stop against the die bottom at the top of the stroke. This will center the case and(most of the time) remove any case runout. If it doesn't then you have problems in the dies or press.

I would also put away the brass you are messing with right now, buy some Lapua, Norma or RWS brass and the Redding FL sizer die at least and start fresh and right to begin with.

You can also toss the expander ball or grind it down, use the "dummy" primer pin holder that usually comes with the bushing dies or buy one from Redding or use a 6.5 expander or smaller so you DON'T touch the neck, THEN use a Sinclair expander rod to open up the neck...Hornady uses an elliptical expander and Lee sizers have a very nice taper to the expander rod...but for gosh sakes if you are going nutz over case neck runout get rid of the "button" and use one or a combination of the others...I do it all the time when I run into difficulties with a particular rifle or set of dies.

I have a set of Hornady, Lee, RCBS and Redding standard and bushing dies for many of my shooters...AND a Wilson straight line seater...plus sliding chambers for my Forster Ultra seater...each is used for it's particular strong points. I like Hornaday sizers and elliptical expanders but the seater sucks...Redding always has excellent sizers but you see the problems with their expanders, the seaters are OK for hunting expectations and even their high dollar, custom micrometer seater isn't all it's cracked up to be...I have 3 sets and the seater stays in the box while I use a Wilson straight line seater...same with RCBS. Lee's sizers and expanders work great without causing major runout problems but the seaters suck also...and I really like the Collet dies for some calibers.

I've been at this game many years and usually start out with the cheaper sets of dies, then get more expensive if needed, so I have ALL the standards covered several times over. I also use Lee dies for case forming when doing some of my wildcats...Totally much cheaper than RCBS forming dies.

Expander balls have been the bain of reloaders from the start and for some reason people get all pig headed thinking they HAVE to use them when there are simple well known workarounds being used for as long as I've been doing this and I learned it from old timers who learned it when THEY were young.

Measure the neck ID of a fired case sized WITHOUT the expander button and see just how much the neck is reduced and what the ID of the neck is...depending on where the tolerances for the chamber reamer and the sizer reamer fall, you might just be able to put a nice bevel on the neck mouth inside with your deburring tool and just seat your bullets without bothering with an "expander"...I've done that on several hunting rifles without any problems, and worked up loads that hit the top end of the velocity spectrum AND 3/4" or slightly less 3-5 shot groups...plenty good enough for deer, sage goats, elk AND sage ratz for practice.

Luck