Bravo1Niner, interesting discussion and one that I'll bet is only vaguely useful. I'm going to assume that you're a reasonably experienced reloader and have set up the sizing die correctly.
So with that, read this thread, it's old but there's good info in there, particularly posts by George.
http://www.brianenos.com/forums/index.php?showtopic=748
In my experience chambering issues is almost never due to the shoulders not being set back enough, it's almost always with the base of the case and mostly deformation around the rim area. I use range brass exclusively so I have no idea of my brass' history, other than it's free, so I expect issues with the brass.
I have three ARs and use the Wilson gauge, if a case or round passes the Wilson gauge, then it will always chamber in my rifles, if it does not pass the gauge, then the round will never chamber in my rifles. That's just my experience and I know I'm likely annoying Mr. Guffey even further by saying that...
Lastly, since you're on a new press - if the Wilson gauge has worked for you in the past and now doesn't - then look to the press set up. If you have a new/different shell holder, I'd look at that as a potential source for sizing errors.
However, if the press is ok, then possibly your rifle chamber is too tight to allow use of the Wilson gauge, Google this gauge for information, it gives you an option for checking brass for a tight chamber, JPCG-223. or go here.
http://www.jprifles.com/buy.php?item=JPCG-223