I think if you expect any kind of accuracy, you need to pay attention to all the small details. It may not help but it can't hurt. I measure runout using a Sinclair gauge. In the picture is a 208 grain Hornady A-Max (a .308 round). I measure 1/2 way out to the tip. My better rounds have .001" total runout or less. I also keep anything .002" but over that gets pulled or used for fouling shots.
As far as sizing the cases, my rifle is cheap and has a lot of neck clearance. I set the shoulders back no more than .001" and figure they center there in the front. I had a Forster full length benchrest die modified and this is how close the resized cases are to a fired one (and compared to a Lee die). The only micrometer I have has flat surfaces so I center it over the edges on the case the best I can. I know it reads off the largest diameter. I do use a sizing ball which leaves a .002" interference fit. The ball floats and does not add any runout.
I use a Redding Competition seating die with a micrometer dial. I seat the depth based on measuring the headspace in the chamber and using a Hornady bullet comparator on a dial caliper, not from the tip, and try to keep them to within .001". It would be better if the tool insert matched the actual chamber contour.
