Go to this post, and scroll down to #61:
http://www.snipershide.com/shooting/sniper-hide-gunsmithing/214393-short-action-284-win-tactical-l-build-shilen-action-barrel-2.html#post3038151
You will see my comments on donuts/neck tension. Not that you are having issues with donuts, but consistent neck tension could also be an issue with some of your flyers. Using pin gages, I can quickly check a batch of re-sized brass to find out if any are over/under sized. This difference in internal neck diameter/neck tension is typically the result of using a bushing die on brass that has varying neck thickness.
It amazes me the number of people that size only with a neck bushing, and no type of internal expander, and expect consistent neck tension? Contrary to popular belief, both internal and external neck measurements can be critical, and only working one of them, will not necessarily guarantee the other.
You really need to check the consistency of the neck thickness in your brass, and that is all around the neck of a single case, as well as from piece to piece. If you have any level of variation, then it can lead to issues with runout and neck tension, both of which could impact accuracy. How much, obviously depends on how bad the variation is.
Only real way to deal with varying neck thickness, is to measure and sort, or neck turn it all to consistent thickness. There are obvious pros & cons to both options.
In most cases, I see people going to this level of preparation/work when they are chasing results in the 0.25-0.50 MOA range. I don't usually see this as being primary issue when you are talking about results that are 1.0 MOA plus. If the issue is that big, it is usually something else.
Not sure if I am reading your original post correctly? But if you are mixing various makes/types of brass into a single loading, there is not much of any chance that you are going to get consistent anything! Just using two different types of brass can result in completely different internal capacities, which translates into different pressures/velocities, which will obviously have a major impact on the results.
If you check the link below, it will show the various case capacities for a number of .308 cases (not sure what cal this is?):
The Rifleman's Journal: Cartridges: 1000 Yard .308 Case Capacity and Other Problems
Per that info, case capacity could range from as low as 53.45 to as high as 57.40.
Hard to track everything that could be going on here without more info, runout may only be one of the issues?