I just full length sized 50 new Winchester case, with a Redding FL die, floating carbide button in place. Results are not good.

For Winchester brass, the cases did not look too bad (or great) averaging around .0015" neck wall thickness variation and .0035" neck runout, right out of the bag. After the resizing, virtually all cases had runout of at least .004", with some at a whopping.008". Is this just endemic to full length sizing dies, or is there something amiss with my procedure? Or, are bushing dies the only way to improve runout? Since it was stated above that bushing dies may not work in ARs, I wonder what AR users are doing to minimize runout.
Thanks.
- Phil