If your fired brass has significant run out forget trying to straighten your reloads.
Gauges that measure loaded rounds at the neck and ogive while holding on the body walls are the best IMHO, ones that hold the base and tip of projectile don't tell you if it is angular misalignment or eccentric neck that is giving the runout.
Actual eccentricity of the neck compared to case is rare if chamber is sweet and dies used correctly, which in the case of un turned brass means the bullet will be offset by the variation in neck thickness.
More common is a concentric neck with a bullet seated slightly at an angle, which if minor is easy enough to correct.
I made myself a jig to measure concentricity and graded my reloads by run out and shot some groups with the worst and some groups with the best, any difference was lost in the noise of my shooting ability so now I just load and shoot.....but this is for hunting. If I was shooting competitively I would take every possible measure to ensure absolute consistency at every step of the reloading operation.
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