You need to test case body and neck runout on fired and resized cases. Meaning check the case body and see if it is egg shaped. If the case body is thinner on one side it will expand more when fired and bulge on that side. Then when resized the case can become banana shaped. Then when you check neck runout or bullet runout you are rotating the case on a egg shaped case body.
This problem becomes worse the more the case body expands when fired increasing how much the case body becomes egg shaped. Many people blame this on the chamber when case wall thickness uniformity is causing the problem. Meaning if the case diameter is on the minimum side of tolerances and the chamber is on the plus side of diameter tolerances the more the case can bulge and warp.
This is what the Redding FAQ was telling you, you can't make a case that does not have uniform case wall thickness shoot better. Below is an example with the case neck on the right. You can turn this case neck "BUT" neck turning does not fix the case body that warps when fired.
Bottom line, are your cases causing the problem or is the chamber causing the warped cases.
NECO CONCENTRICITY, WALL THICKNESS AND RUNOUT GAUGE
Also referred to as "The Case Gauge," this item is designed to measure:
1) The curved "banana" shape of the cartridge case;
2) The relative wall thickness variation of a cartridge case;
3) The cartridge case head out-of-squareness;
4) Individual Bullets – out-of-round "egg shape" and/or
curved "banana" shape (excepting very small bullets);
5) The seated bullet and cartridge runout of loaded rounds. The accuracy of any firearm is determined — and limited — by the quality of the ammunition shot in it. The effect of imperfections in ammunition is cumulative; each flaw adds to the influence of all others. Precision shooters spend much time and effort "uniforming" cartridge cases, using advanced techniques to eliminate variation. Yet until recently, one of the most important of these variations has not been susceptible to detection by any device readily available to marksmen.