Hi,
I'm not sure how much concentricity's a function of the die's innards and how much is the thread interface between the die and press.
Someone taught be about that aspect years ago, and suggested I always try to have some kind of "pressure" between the shellholder and die BEFORE tightening the lock ring.
For example, instructions for my depriming dies (Lee, rifle) say the dies should be screwed in until they "touch" the shellholder, then add 1/4 turn or so. Which means I'd have the ram raised to the top, screw the die down until it touches, then lower the ram a bit to add the 1/4 turn. At this point, the "ol' timer" told me to raise the ram again, and hold it, squaring the die up in the threads relative to the shellholder, and hold it all tight while I tightened the lock ring.
W/ dies that "just touch" such as carbide sizing dies, I'll stick a business card between the shellholder and die to be able to exert some pressure when I raise the ram, then tighten the lock ring.
It's not a perfect system, but certainly takes a fair amount of "slop" out of some of the die/press combos I use and I no longer turn the cases during seating or sizing like I sometimes used to....
A side benefit is it's often easier to start unscrewing the dies if one first puts a little upward pressure on them, too!
Rick C