I have the Hornady L-n-L classic press that uses there bushings and I get no movement when sizing . Now there is movement when pulling the case out of the die but the sizing has already been done . If you are seeing what I think you're seeing it has no effect on the consistency of you sized cases . There is no movement when the ram is going up or you are sizing the case , it's when the ram pulls on the bushing and the O-ring compresses that's the movement you see . If it's just that they tend to back out/turn counter clockwise a tad over many multiple sizing's . Yes mine does to , That's just the by product of having that slip fit . I just keep an eye on it and snug it up every once and awhile .
I have found the biggest obstacle to consistent case sizing ( from head to datum point ) with the Hornady press is the press flex or deflection in the handle to ram linkage . With my type you must have hard contact between shell holder and die with cam over .
Here are two pics showing the deflection I'm talking about . The first is showing the die screwed down to just make contact with the shell holder when ram is fully up . The second is sizing a 308 case with the die in that same setting . Notice the gap that appears when you put stress on the press do to the sizing process
The problem one can run into with hard contact with cam over using a standard shell holder is your shoulders get bumped back further then you want . I have found using the Redding competition shell holders completely eliminates this problem by allowing the hard contact between die and shell holder while still being able to size your cases longer ( from head to datum point ) in increments of .002 depending on the shell holder you use .
When using this method my cases are sized to with in +/- .001 of each other from head to datum point and the vast majority of them come out +/- .0005 from one another . If you are getting inconsistently sized cases . My bet is that it not the bushing system that is causing the problem .
I don't use the Iron press so all this may mean nothing but thought I'd put it out there in case it does .