Re: Excessive run out.....
There are many factors that can affect run-out of final loaded cartridges. Some as simple as technique and some as complex as equipment or component alignments.
Technique: If you're just running the ram up and down, you're missing out on a lot. With my entry-level RCBS press I noticed that if I cam-over too hard to where I felt the handle bump solid into the stop, it would induce run-out in that round. With good technique (start the bullet as straight as possible, rotate the case a few times DURING seating (not just at the end), go SLOW, barely cam-over) that my o-give consistency and runout were greatly improved. I was producing runout of .000-.002" in a cheap RCBS press with Redding competition dies and unturned .308 Lapua cases.
Recently I purchased a Redding T7 press and despite my best efforts I was seeing runout of .006-.007". I scratched my head for days wondering what could be going on... Is there too much slop in the rotating head?... Are the die stations perfectly in line with the ram?... Turns out the answer was easier than I expected. I noticed that the shell holder "snapped" into the Redding ram very forcefully compared to my old RCBS press. I removed the snap-ring and instantly runout was back down to within two thousandths and can easily be corrected from there with the Hornady Concentricity gauge. I now use a rubber o-ring around the entire ram to keep the shell holder from falling out and allow the holder to float freely in the press.
The Hornady tool is great for measuring final runout on loaded cartridges but does have its limitations. Some prefer to run the dial indicator on the bullet, others run it on the case. There are several schools of thought on which measurement is the most critical but test your processes using both methods and see what produces the best results for YOU.
A bare-case concentricity gauge is also helpful to check things as the reloading process progresses. Check your fired cases right out of the gun. Check your cases after neck-sizing or full length resizing if that's what you're into. Also, depending on brass quality, check your neck thickness variations.
Unfortunately there may be several of these factors adding into the equation. Experiment with these many factors and you'll likely find the "smoking gun" that is causing your troubles.
My $.02
Tony P.