have you checked your fired case for runout ? You should . Also recheck neck thickness again , Mark the cases with the most runout . A case will usually banana if one side is thicker than the other . Use these for sighters . You must have hit the lottery with your brass , remember I also shoot Lapua 7.62 x53 brass . The rules don't change . You headspace off the shoulder , if you insert a round bullet into an off center case mouth , then try to straighten the bullet , the neck which isn't concentric will be forced to be ,by the tool, by doing so will change the shoulder . The case body I think would also be straightened , so the shoulder is now not even . And this is what your head spacing off of .
What happens if you check runout as near the rim as possible ? What is the runout at the .200 mark , how about at the rim ?
The picture you posted of the burnished case neck ,along with your statement is useless . You must eliminate variables to come to such a broad statement .
Check cases , eliminate the worse , turn necks on those that are acceptable , then if your fired case have acceptable runout , rerun your test . Maybe as a blind test . Use marks ,small scratches on rim and have a friend hand you random cases . Use a large number of groups in varying conditions . Use wind flags , use a good bench or prone with a good front rest and rear bag . There are no shortcuts , if you think so your fooling yourself .
What is your chambers neck Diam? Should be on reamer print . What is your loaded round neck diam ? What is your sized neck diam , bullet diam , tension ?
Your choice of actions and the rimed round are a challenge .
Good luck