Generally, when I measure my loaded ammo (for my 6PPC) I have around .0015 runout, about .150 from the end of the case neck. As far as I can tell, this seems to be OK.
Some years ago, I did a little measuring of my Wilson seater. I wrapped scotch tape around the case neck until I could feel some resistance as I inserted it in the die, and then measured the wrapped neck. Another thing that I did was to see how far a case would go into the die base first. My conclusion was that the die was a pretty loose fit, probably because they are made to fit neck sized brass, from any chamber. Other measurements that I did convinced me that using a shallow VLD chamfer helped, as did minimal neck tension, and boat tail bullets, but since I use flat base bullets, and a lot of neck tension, I concluded that I needed a tighter fitting die. About that time, I was shooting a match at Visalia, and Don Nielson had brought several seating dies with him, to sell. He let me try one that has a .262 neck and a tighter fitting body, and my ammunition's concentricity improved to what I mentioned above, and it seemed to me that my groups were slightly improved. In any case, being an impatient sort, with my only other alternative being a custom chambered seater, I bought the die, (for $150, if I remember correctly). It doesn't have a micrometer, but I soon learned to slightly loosen the stem set screw and change the OAL of the stem and cap and then very lightly snug the set screw. I really don't miss the micrometer.
One of these days, I will probably try some of the newest short boat tail bullets that some are shooting so well. Based on earlier experience, i would guess that one advantage is that they would seat straighter on average.
One more thing, I you are having concentricity issues with a bushing FL die, a one piece die that has the correct neck dimension should resolve your problem. I know that this takes away the option of changing neck tension by changing bushings, but since I tend to only tune with powder and seating depth, for me this is not a problem. I have played around with a Hornady one piece FL die, and its neck is serviceable for a .262 chamber...very straight brass, and inexpensive.